Area is a chapter in the CBSE Class 8 Mathematics syllabus from Ganita Prakash Part II. This chapter hub brings together revision notes, practice questions, worksheets, flashcards, formula sheet to help students learn, practice, and revise Area effectively.

Scroll down to find Area notes, practice questions, worksheets, and revision resources — all in one place. Use the sidebar to jump to any section, or browse the full page below.

Area

NCERT Class 8 Mathematics Chapter 7: Area (Pages 150–171)

Summary of Area

Playing 00:00 / 00:00

Area at a Glance

Board

CBSE

Class

Class 8

Subject

Mathematics

Book

Ganita Prakash Part II

Chapter

7

Pages

150171

Resources

7 study resources

Area Summary

In this chapter, students explore the concept of area and its significance in measuring surfaces. The focus is primarily on rectangles and triangles, as these shapes commonly appear in everyday life and various mathematical applications. The chapter begins by illustrating how to divide a square into four equal parts, prompting students to think creatively about area distribution. This introduction emphasizes that these partitions can maintain equal areas even when shapes are manipulated. Students learn that the area of a rectangle is found by multiplying its length and width. This formula is demonstrated with examples, showing how different rectangles can be compared based on their area. For instance, the understanding of area is linked to familiar activities, such as coloring a rangoli, where the amount of powder used corresponds to the area being covered. The chapter also addresses how to find the area of triangles. Students discover that the diagonal of a rectangle divides it into two congruent triangles, leading to the realization that the area of each triangle is half that of the rectangle. The formula for the area of a triangle is introduced, highlighting the importance of knowing the base and height to compute the area efficiently. Building on these concepts, the chapter challenges students to consider why perimeter cannot be a measure of area. It guides them through thought-provoking questions, such as whether two regions with the same perimeter must also have the same area. Through examples, students learn that it is possible for two different shapes to have the same perimeter while exhibiting varying areas, broadening their understanding of geometrical properties. Various exercises and problems encourage students to apply their learning in real-world contexts. For example, students will measure the area of shaded paths around rectangular parks, analyze different triangles, and engage with applications from historical texts like the Śulba-Sūtras, which delve into ancient geometry. Overall, this chapter establishes foundational knowledge of area measurement, guiding students to derive solutions, compare areas, and understand the real-world relevance of mathematics.

Area Revision Guide

Download the Area revision guide with key points, summaries, and quick revision notes for CBSE Class 8 Mathematics.

Key Points

1

Define Area.

Area is the extent of a surface, measured in square units. Use unit squares for calculation.

2

Area of a Rectangle.

Area = length × width. Example: For a rectangle of 7 cm and 4 cm, area = 28 cm².

3

Area of a Triangle.

Area = 1/2 × base × height. For a height of 4 cm and base of 3 cm, area = 6 cm².

4

Congruent Triangles.

Triangles are congruent if they have the same area. Diagonal of a rectangle forms two congruent triangles.

5

Dividing Squares.

A square can be divided into four equal-area parts creatively. Explore different divisions for insight.

6

Perimeter vs. Area.

Perimeter does not reflect area. Two figures can have the same perimeter but different areas.

7

Rangoli and Area.

To decorate areas like rangoli, calculate required area using unit squares. Example: 28 cm² needs more color.

8

Rectangles with Paths.

A path around a rectangle can be calculated using the outer rectangle’s area minus the inner park's area.

9

Finding Missing Sides.

To determine areas, identify missing lengths needed to compute area formulas correctly.

10

Area Increase with Doubling.

Doubling the side length of a square quadruples the area. Example: 2 cm to 4 cm leads from 4 cm² to 16 cm².

11

Identical Rectangles.

Identical rectangles have equal areas. Checking congruence proves equality.

12

Effects of Shape on Area.

Same perimeter, different shapes yield different areas. Explore rectangles versus circles for examples.

13

Area of Composite Figures.

Break complex shapes into simpler ones (like rectangles and triangles) for area calculation.

14

Triangles Between Parallel Lines.

Finding maximum and minimum areas can involve heights from a base. Explore variations for insights.

15

Area Transformations.

In ancient methods, transform shapes while maintaining equal area. Example: Rectangle to triangle.

16

Piece Movement and Area.

Moving pieces like in spatial puzzles can help visualize area conservation. Engage physically for learning.

17

Height from Non-Baseline Vertices.

In triangles, heights can drop from non-base vertices, adjusting expected area calculations.

18

Fractional Areas.

Understanding area fractions is key. For instance, midpoints can reduce total area by half.

19

Visualizing with Grid.

Using grid paper aids in visualizing unit squares, helping with area calculations effectively.

20

Shortest Path Problems.

Real-world applications, like Gopal's path, illustrate area and distances in practical scenarios.

Area Practice Questions & Answers

Practice important questions and exam-style problems from Area. These questions cover key topics from the CBSE Class 8 Mathematics syllabus.

How to practice: Start with the questions below to test your understanding of Area. Use the revision guide to review concepts you find difficult, then come back and retry the questions for better retention.

View all 121 Area questions
Q9

A rectangle has dimensions that are twice the length and half the width of a square with a side of 4 cm. What is the area of the rectangle?

Single Answer MCQ
Q-00134084
View explanation
Q10

What is the area in square centimeters of a rectangle with a length of 7 cm and a width of 3 cm?

Single Answer MCQ
Q-00134085
View explanation
Q11

Which of the following shapes has the largest area if their dimensions are as follows: Rectangle 1: 2 cm x 5 cm; Rectangle 2: 3 cm x 4 cm; Rectangle 3: 1 cm x 8 cm?

Single Answer MCQ
Q-00134086
View explanation
Q12

If you have a square divided into four smaller squares, what is the area of one smaller square if the side length of the large square is 12 cm?

Single Answer MCQ
Q-00134087
View explanation
Q13

What is the area of a rectangle with a length of 8 cm and a breadth of 5 cm?

Single Answer MCQ
Q-00134088
View explanation
Q14

If a square's area is 25 cm², what is the length of one side of the square?

Single Answer MCQ
Q-00134089
View explanation
Q15

Two rectangles both have equal area of 30 cm². Which condition could NOT be true?

Single Answer MCQ
Q-00134090
View explanation
Q16

How many square centimeters are in 1 m²?

Single Answer MCQ
Q-00134091
View explanation
Q17

What is the formula for the area of a triangle?

Single Answer MCQ
Q-00134092
View explanation
Q18

If the base of a triangle is 10 cm and its height is 5 cm, what is its area?

Single Answer MCQ
Q-00134093
View explanation
Q19

Which of the following statements about triangles and area is correct?

Single Answer MCQ
Q-00134094
View explanation
Q20

What is the area of a rectangle with length 5 cm and width 3 cm?

Single Answer MCQ
Q-00134095
View explanation
Q21

If a triangle has a base of 8 cm and a height of 6 cm, what will be the area?

Single Answer MCQ
Q-00134096
View explanation
Q22

A rectangle has a length that is double its width. If the width is 4 cm, what is its area?

Single Answer MCQ
Q-00134097
View explanation
Q23

In a rectangle ABCD, two triangles ABD and ABC are formed using diagonal AC. How do their areas compare?

Single Answer MCQ
Q-00134098
View explanation
Q24

If the dimensions of a rectangle are increased by 3 cm each, how will its area change if the original dimensions were 10 cm and 5 cm?

Single Answer MCQ
Q-00134099
View explanation
Q25

What happens to the area of a triangle if its base is doubled and the height remains the same?

Single Answer MCQ
Q-00134100
View explanation
Q26

What is the area of a rectangle that has a length of 9 meters and a width of 6 meters?

Single Answer MCQ
Q-00134101
View explanation
Q27

Which triangle will have the maximum area among those sharing the same base but different heights?

Single Answer MCQ
Q-00134102
View explanation
Q28

A rectangle has an area of 48 cm². If its length is 8 cm, what is its width?

Single Answer MCQ
Q-00134103
View explanation
Q29

If triangle XYZ has an area of 40 cm² and its base is 8 cm, what is its height?

Single Answer MCQ
Q-00134104
View explanation
Q30

Which of the following rectangles has the largest area: 6 cm by 7 cm, 5 cm by 8 cm, or 4 cm by 9 cm?

Single Answer MCQ
Q-00134105
View explanation
Q31

Triangles ABC and DEF both share line segment BC as a common base. If their heights are in a ratio of 2:3, what is the ratio of their areas?

Single Answer MCQ
Q-00134106
View explanation
Q32

If a rectangle's length is decreased by 2 cm and its width is increased by 2 cm, what will happen to its area?

Single Answer MCQ
Q-00134107
View explanation
Q33

A triangle has sides of 6 cm, 8 cm, and 10 cm. What is its area?

Single Answer MCQ
Q-00134108
View explanation
Q34

A rectangle is 3 times as long as it is wide, and the perimeter of the rectangle is 48 cm. What is the area?

Single Answer MCQ
Q-00134109
View explanation
Q35

What is the area of a triangle if the base is 12 cm and the height is 9 cm?

Single Answer MCQ
Q-00134110
View explanation
Q36

What is the relationship between the areas of a rectangle and the triangles formed by its diagonals?

Single Answer MCQ
Q-00134111
View explanation
Q37

Which configuration of triangles will yield the same area but different heights?

Single Answer MCQ
Q-00134112
View explanation
Q38

A rectangular garden has dimensions of 12 m and 10 m. How many 1 m² tiles are needed to cover the garden?

Single Answer MCQ
Q-00134113
View explanation
Q39

How can one prove that triangles formed by drawing diagonals in a rectangle have equal areas?

Single Answer MCQ
Q-00134114
View explanation
Q40

If the area of a rectangle is expressed as 45 cm² and the length is 9 cm, what is the width?

Single Answer MCQ
Q-00134115
View explanation
Q41

If a triangle's area is known to be 36 cm² and its base is 12 cm, what is the height?

Single Answer MCQ
Q-00134116
View explanation
Q42

What is the area of a rectangle whose length is increased by 5 cm and width by 2 cm from its initial dimensions of 10 cm and 2 cm?

Single Answer MCQ
Q-00134117
View explanation
Q43

What will be the area of triangle ABC if its base is doubled while keeping height constant?

Single Answer MCQ
Q-00134118
View explanation
Q44

Which property is true about the area of identical rectangles?

Single Answer MCQ
Q-00134119
View explanation
Q45

In a right triangle with a base of 9 cm and a height of 12 cm, finding its area requires what?

Single Answer MCQ
Q-00134120
View explanation
Q46

A rectangle has an area of 100 cm². If the width is halved, what happens to the area?

Single Answer MCQ
Q-00134121
View explanation
Q47

A farmer has a rectangular field measuring 20 m by 10 m. If he wants to add a 2 m wide path around the field, what will be the new area?

Single Answer MCQ
Q-00134122
View explanation
Q48

What is the formula for the area of a rhombus?

Single Answer MCQ
Q-00134123
View explanation
Q49

If the diagonals of a rhombus are 8 cm and 6 cm, what is its area?

Single Answer MCQ
Q-00134124
View explanation
Q50

A rhombus has an area of 50 cm² and one diagonal of 10 cm. What is the length of the other diagonal?

Single Answer MCQ
Q-00134125
View explanation
Q51

If a rhombus has an area of 32 cm² and the length of one side is 8 cm, can the shape be a rectangle?

Single Answer MCQ
Q-00134126
View explanation
Q52

Which statement about the area of a rhombus is incorrect?

Single Answer MCQ
Q-00134127
View explanation
Q53

What property allows you to divide a rhombus into congruent triangles?

Single Answer MCQ
Q-00134128
View explanation
Q54

If a rhombus has sides of length 10 cm and an angle of 60°, what is the area?

Single Answer MCQ
Q-00134129
View explanation
Q55

Can the area of a rhombus be calculated using only its perimeter?

Single Answer MCQ
Q-00134130
View explanation
Q56

In what scenario is the area of a rhombus maximum given a fixed perimeter?

Single Answer MCQ
Q-00134131
View explanation
Q57

If the diagonals of a rhombus are in a ratio of 2:1, and the longer diagonal is 12 cm, what is the area?

Single Answer MCQ
Q-00134132
View explanation
Q58

How does changing the angle between the diagonals affect the area of the rhombus?

Single Answer MCQ
Q-00134133
View explanation
Q59

Which of the following represents the relationship between the area, diagonals, and angles in a rhombus?

Single Answer MCQ
Q-00134134
View explanation
Q60

If the area of a rhombus is 'x' and its longer diagonal is 'd1', what expression represents the shorter diagonal 'd2'?

Single Answer MCQ
Q-00134135
View explanation
Q61

What is the area of a rectangle with length 8 cm and width 5 cm?

Single Answer MCQ
Q-00134136
View explanation
Q62

If the dimensions of a rectangle are doubled, how does the area change?

Single Answer MCQ
Q-00134137
View explanation
Q63

What is the area of a triangle with a base of 10 m and a height of 5 m?

Single Answer MCQ
Q-00134138
View explanation
Q64

Which of the following has the greatest area: a rectangle of 12 cm by 8 cm or a triangle with a base of 12 cm and height of 8 cm?

Single Answer MCQ
Q-00134139
View explanation
Q65

A rectangle has a length that is twice its width. If the width is 4 cm, what is the area?

Single Answer MCQ
Q-00134140
View explanation
Q66

What is the area of a parallelogram with a base of 15 m and height of 6 m?

Single Answer MCQ
Q-00134141
View explanation
Q67

If two triangles have the same base but different heights, which has the larger area?

Single Answer MCQ
Q-00134142
View explanation
Q68

What measurement is essential to calculate the area of a trapezoid?

Single Answer MCQ
Q-00134143
View explanation
Q69

In a triangle, if one side is 10 cm and the opposite height is 5 cm, what is the area?

Single Answer MCQ
Q-00134144
View explanation
Q70

What is the area of a square with a side length of 3 m?

Single Answer MCQ
Q-00134145
View explanation
Q71

A rectangle has a perimeter of 40 m and a length of 15 m. What is its width?

Single Answer MCQ
Q-00134146
View explanation
Q72

The area of a trapezoid is given as 50 m² with bases measuring 10 m and 6 m. What is the height?

Single Answer MCQ
Q-00134147
View explanation
Q73

If a triangle has sides of lengths 8 cm, 6 cm, and 10 cm, how can you determine its area?

Single Answer MCQ
Q-00134148
View explanation
Q74

What happens to the area of a square if each side is increased by 50%?

Single Answer MCQ
Q-00134149
View explanation
Q75

What is the area of an irregular polygon with known side lengths of a triangle, base 10 cm, height 4 cm?

Single Answer MCQ
Q-00134150
View explanation
Q76

When calculating the area of a parallelogram, if the height is halved, what happens to the area?

Single Answer MCQ
Q-00134151
View explanation
Q77

What is the formula for the area of a trapezium?

Single Answer MCQ
Q-00134152
View explanation
Q78

What is the formula for the area of a parallelogram?

Single Answer MCQ
Q-00134153
View explanation
Q79

If one base of a trapezium measures 5 cm, the other base measures 3 cm, and the height is 4 cm, what is the area?

Single Answer MCQ
Q-00134154
View explanation
Q80

If the base of a parallelogram is doubled and the height remains the same, how does the area change?

Single Answer MCQ
Q-00134155
View explanation
Q81

A trapezium has bases of lengths 10 cm and 6 cm, with a height of 5 cm. Calculate the area.

Single Answer MCQ
Q-00134156
View explanation
Q82

A parallelogram has a base of 10 cm and a height of 5 cm. What is its area?

Single Answer MCQ
Q-00134157
View explanation
Q83

If a trapezium has an area of 50 cm², one base is 8 cm, and the height is 5 cm, what is the length of the other base?

Single Answer MCQ
Q-00134158
View explanation
Q84

Which of the following statements about the area of a parallelogram is true?

Single Answer MCQ
Q-00134159
View explanation
Q85

Which of the following statements is true about the area of a trapezium?

Single Answer MCQ
Q-00134160
View explanation
Q86

What happens to the area of a parallelogram when the height is tripled while keeping the base constant?

Single Answer MCQ
Q-00134161
View explanation
Q87

A trapezium's bases are 9 cm and 5 cm, and its height is 3 cm. What expression gives its area?

Single Answer MCQ
Q-00134162
View explanation
Q88

If the area of a parallelogram is 36 cm² and the base is 6 cm, what is the height?

Single Answer MCQ
Q-00134163
View explanation
Q89

Calculate the height of a trapezium if the area is 120 cm², bases are 10 cm and 14 cm.

Single Answer MCQ
Q-00134164
View explanation
Q90

A parallelogram and a rectangle have the same base and height. Which of the following is true?

Single Answer MCQ
Q-00134165
View explanation
Q91

A trapezium has an area of 36 cm² and bases of 4 cm and 10 cm. What is the height?

Single Answer MCQ
Q-00134166
View explanation
Q92

How can the area of a parallelogram be visually interpreted?

Single Answer MCQ
Q-00134167
View explanation
Q93

Consider a trapezium divided into two triangles. How can you express the area of the trapezium using these triangles?

Single Answer MCQ
Q-00134168
View explanation
Q94

Which of the following is a common misconception regarding parallelograms?

Single Answer MCQ
Q-00134169
View explanation
Q95

A trapezium has bases of lengths 3 cm and 7 cm, and an unknown height. If the area is 25 cm², what is the height?

Single Answer MCQ
Q-00134170
View explanation
Q96

If a rhombus is a special type of parallelogram with diagonals intersecting at right angles, what can be said about its area?

Single Answer MCQ
Q-00134171
View explanation
Q97

Is it possible for two trapeziums to have the same area but different heights? Why?

Single Answer MCQ
Q-00134172
View explanation
Q98

What is the area of a parallelogram with a base of 12 cm and a height of 10 cm?

Single Answer MCQ
Q-00134173
View explanation
Q99

Find the area of a trapezium whose bases are 12 cm and 18 cm, with a height of 4 cm.

Single Answer MCQ
Q-00134174
View explanation
Q100

A parallelogram with a base of 15 m has an area of 75 m². What is its height?

Single Answer MCQ
Q-00134175
View explanation
Q101

A trapezium has an area of 100 cm², one base as 20 cm, and a height of 10 cm. What could be the length of the other base?

Single Answer MCQ
Q-00134176
View explanation
Q102

What geometric shape is formed by connecting the midpoints of the sides of a parallelogram?

Single Answer MCQ
Q-00134177
View explanation
Q103

If the height of a parallelogram is decreased by half, what effect does it have on the area?

Single Answer MCQ
Q-00134178
View explanation
Q104

In terms of area, how do a square and parallelogram of equal base and height compare?

Single Answer MCQ
Q-00134179
View explanation
Q105

A parallelogram's area is calculated using which of the following?

Single Answer MCQ
Q-00134180
View explanation
Q106

What is the area of triangle ABC if AX = 5 units and BC = 6 units?

Single Answer MCQ
Q-00134181
View explanation
Q107

If the area of triangle ABC is 20 sq. units and the base BC is 8 units, what is the height AX?

Single Answer MCQ
Q-00134182
View explanation
Q108

What is the length of BY if the area of triangle ABC is 15/2 sq. units and AC = 4 units?

Single Answer MCQ
Q-00134183
View explanation
Q109

Are the areas of the four triangles formed by the diagonals of a rectangle equal?

Single Answer MCQ
Q-00134184
View explanation
Q110

Which triangle has the minimum perimeter when BC is the base and the third vertex lies on a line parallel to BC?

Single Answer MCQ
Q-00134185
View explanation
Q111

If OD = 3 units in a rectangle and both diagonals intersect at point O, what are the areas of triangles formed by diagonal OB?

Single Answer MCQ
Q-00134186
View explanation
Q112

If triangle ABC has sides AB = 6 units, BC = 4 units, and height from A to base BC = 3 units, what is its area?

Single Answer MCQ
Q-00134187
View explanation
Q113

In a rectangle, the length is twice the width. If the width is 3 units, what is the area?

Single Answer MCQ
Q-00134188
View explanation
Q114

What is the height of triangle ABC if base BC = 6 units and area = 12 sq. units?

Single Answer MCQ
Q-00134189
View explanation
Q115

Which configuration of triangle ABC provides the maximum area for a given base and height?

Single Answer MCQ
Q-00134191
View explanation
Q116

For triangles sharing a common base, which triangle has the greatest height?

Single Answer MCQ
Q-00134193
View explanation
Q117

If triangle ABC has its base BC of length x and height h perpendicular to BC, what is a general expression for its area?

Single Answer MCQ
Q-00134195
View explanation
Q118

If a triangle’s sides are 6, 8, and 10 units, is it a right triangle and what is its area?

Single Answer MCQ
Q-00134197
View explanation
Q119

What is the relationship between the heights of triangles sharing the same base?

Single Answer MCQ
Q-00134199
View explanation
Q120

Which statement about triangles formed by cutting a rectangle with a diagonal is false?

Single Answer MCQ
Q-00134201
View explanation
Q121

If two triangles have equal bases and heights but are different otherwise, what can be said about their areas?

Single Answer MCQ
Q-00134203
View explanation

Area Practice Worksheets

Download and practice Area worksheets to improve problem-solving accuracy and speed for CBSE Class 8 Mathematics exams.

Area - Practice Worksheet

This worksheet covers essential long-answer questions to help you build confidence in Area from Ganita Prakash Part II for Class 8 (Mathematics).

Practice

Questions

1

Define the area of a rectangle and explain how to calculate it. Provide examples of rectangles with different dimensions and calculate their areas.

The area of a rectangle is defined as the amount of space enclosed within its four sides. It is calculated using the formula Area = Length × Width. For example, if a rectangle has a length of 5 cm and a width of 3 cm, its area is 5 × 3 = 15 cm². If another rectangle has a length of 7 cm and a width of 4 cm, its area would be 7 × 4 = 28 cm². Thus, the area can vary based on length and width.

2

What is the significance of unit squares in measuring area? Explain with examples.

Unit squares are the basic building blocks for measuring area, where each square has an area of 1 square unit. When determining the area of a larger shape, we can count the number of unit squares that can fit inside it. For instance, in a 4 cm by 3 cm rectangle, 12 unit squares can fit, confirming that the area is 12 cm². Additionally, if a square measures 2 cm on each side, its area is 4 cm², consisting of 4 unit squares.

3

Explain how to divide a rectangle into triangles and calculate the area of each triangle formed by the diagonal. Provide a specific example.

A rectangle can be divided into two triangles by drawing a diagonal from one corner to the opposite. Each triangle will have the same area. Using a rectangle with dimensions 6 cm (length) and 4 cm (width), the area of the rectangle is 24 cm². Hence, each triangle has an area of 24 cm² / 2 = 12 cm². This illustrates how geometric figures can be analyzed based on their partitions.

4

Discuss the relationship between perimeter and area in shapes. Why can’t perimeter be used as a measure of area?

Perimeter is the total length of the boundary of a shape, while area measures the extent of space inside it. Two shapes can have the same perimeter but very different areas, such as a long rectangle compared to a square. For example, a rectangle with a perimeter of 20 cm could have many different dimensions leading to varied areas. This demonstrates that perimeter alone does not determine the size of the space within a shape.

5

Identify various ways to divide a square into four parts of equal area. Provide examples and calculate the area of each part.

A square can be divided into four equal areas through various methods such as bisecting it both horizontally and vertically, or creating diagonal cuts. For instance, a square with a side length of 4 cm has an area of 16 cm². Dividing it into four equal parts results in each part having an area of 16 cm² / 4 = 4 cm². This flexibility in division illustrates the concept of equal areas in geometry.

6

Explain how to calculate the area of a triangle. Provide a formula and example problems with solutions.

The area of a triangle can be calculated using the formula Area = (Base × Height) / 2. For example, if a triangle has a base of 10 cm and a height of 5 cm, the area would be (10 × 5) / 2 = 25 cm². Another example with a base of 8 cm and a height of 4 cm results in an area of (8 × 4) / 2 = 16 cm², demonstrating versatility in calculating the area based on different inputs.

7

How can we validate the area of triangles whether they are congruent by comparing their bases and heights? Provide examples.

If two triangles are congruent, they have the same area regardless of their positioning. We can validate their areas by confirming equal base lengths and correspondingly equal heights. For instance, Triangle A with a base of 4 cm and height of 3 cm has an area of (4 × 3) / 2 = 6 cm². Triangle B, if congruent with the same base and height, will also yield an area of 6 cm², validating the relationship between congruency and area.

8

Discuss the concept of area transformation as presented in the Śulba-Sūtras. Provide one method to convert a rectangle to a triangle with equal area.

The Śulba-Sūtras describe various methods for transforming shapes to maintain equal areas. To convert a rectangle to a triangle, one can take the rectangle's base as one side of the triangle while using the rectangle's height for the triangle peak. For instance, a rectangle measuring 12 cm by 4 cm (area 48 cm²) can transform into a triangle with the same base and height, thus Area = (12 × 4) / 2 = 24 cm², confirming the equal area principle.

9

In practical terms, how can one apply the area concepts in real-life situations, such as planning a garden? Provide a specific example.

Area concepts are crucial in planning spaces like gardens. For example, if planning a rectangular garden of 10 m by 5 m, the area signifies how much space is available for planting. The area is 10 × 5 = 50 m². To ensure coverage with soil or grass, knowing the area allows for accurate calculations of the necessary materials, demonstrating the relevance of area in effective space management.

Area - Mastery Worksheet

This worksheet challenges you with deeper, multi-concept long-answer questions from Area to prepare for higher-weightage questions in Class 8.

Mastery

Questions

1

How can you creatively divide a square into four parts of equal area? Provide multiple methods and illustrate each with a diagram. Is there a connection to the transformation of shapes when you alter the dimensions?

You can divide a square into four equal areas by various means like drawing two perpendicular lines intersecting at the center, or through varying shapes compressing and expanding while keeping equal areas. Diagrams should reflect each method. An understanding of congruence and area conservation is key.

2

In two rectangles with dimensions 7 cm x 4 cm and 8 cm x 3 cm, explain which requires more painting material based on area. Construct a logical argument and show calculations related to unit squares.

The area of the first rectangle is 7 × 4 = 28 cm², and the second is 8 × 3 = 24 cm². Hence, the first rectangle requires more paint. Sketching the rectangles with unit squares would visually represent this conclusion.

3

Explore why perimeter cannot be a reliable measure for area. Provide examples of shapes with identical perimeters yet differing areas. Illustrate your findings with diagrams.

For example, consider two rectangles: one 6 cm x 3 cm and another 5 cm x 4 cm. Both have a perimeter of 18 cm, but their areas differ (18 cm² and 20 cm², respectively). Draw these examples to show this relationship graphically.

4

If a rectangle is divided into two triangles by drawing a diagonal, demonstrate the method to find the area of one triangle. Illustrate with calculations.

The area of the rectangle is length x width (e.g., 7 cm x 4 cm = 28 cm²), thus each triangle's area is half: 28 cm² / 2 = 14 cm². Provide a triangle cut from the rectangle to emphasize symmetry.

5

Determine the area of a path surrounding a rectangular park. Discuss the measurements needed and create both a formula and a sample computation.

Identify the park as a rectangle with dimensions (e.g., 10 m x 5 m). The area of the path can be found using the outer rectangle dimensions minus inner rectangle dimensions. Draw both rectangles to simplify understanding.

6

Calculate the area for triangles positioned between parallel lines using a common base. Discuss how the height impacts the area of these triangles.

The area can be modeled as parallel lines with a fixed base and varying heights. Use the area formula A = 1/2 × base × height and graphically illustrate to compare areas. Demonstrating maximum and minimum areas can clarify understanding.

7

Given two identical triangles within rectangles, prove the equality of their areas using a logical argument based on congruence and shared dimensions.

Show that both triangles share the same base and height, thus proving Area = 1/2 × base × height for each gives identical area outputs. Diagrams should clearly represent these attributes.

8

If the sides of a square are doubled, illustrate the increase in areas of internal regions, providing numerical examples and reasoning.

For a square of side length 2 cm, original area = 4 cm². If doubled, new area = 16 cm². The increase in area can be calculated as 16 cm² - 4 cm² = 12 cm², emphasizing the area growth proportional to the square of the side length change.

9

Design a cross-path on a rectangular plot. Discuss how to determine its area based on the dimensions provided. Use sample values to demonstrate computing the total area.

Identify the dimensions of the primary rectangular plot; for example, 14 m x 12 m. Outline geometrical relations required to determine cross-path area considering intersections. Provide illustrative examples.

10

Reflect on how altars depicted in ancient texts can help in constructing geometric shapes of equal areas from given shapes. Provide a structured method for such transformations.

Use examples from the Śulba-Sūtras, such as transforming a rectangle into a triangle of equal area by preserving height or adapting bases. Demonstrate these transformations with calculations.

Area - Challenge Worksheet

The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Area in Class 8.

Challenge

Questions

1

Discuss the various methods to divide a square into 4 equal-area parts and evaluate the potential applications of these methods in real-world contexts.

Consider geometric transformations and their implications for design, art, and efficiency. Use examples like architecture or landscape planning to illustrate your points, and analyze alternative approaches.

2

How does the area of a rectangle relate to its perimeter, and why can't perimeter be used as a reliable measure of area? Provide examples with varying dimensions.

Evaluate the relationship through comparisons of different rectangles and discuss scenarios where two shapes may share the same perimeter but differ in area.

3

Create a real-world scenario where measuring the area of a crosspath around a rectangular park is essential. What measurements would you take, and how could you calculate the area of the path?

Formulate a response that explains the necessary steps and possible values for dimensions, while considering an equation to represent the calculation.

4

Explore the implications of doubling the dimensions of a square on the areas of four triangles formed by its diagonals. Quantify the changes and explain why this occurs.

Analyze the resulting areas of the triangles post-expansion, supporting your answer with mathematical reasoning and visualization.

5

Evaluate the comparative areas of triangles formed by different baselines and heights within a rectangle. What can this tell us about the principles of triangle area calculations?

Use specific numerical examples to validate the formulas, and discuss implications for understanding area in various geometries.

6

Investigate the area of a spiral tube and propose methods for accurately calculating it. Which parameters significantly impact your results?

Detail various approaches for area estimation, emphasizing the importance of consistent width and length measurements.

7

Contrive a mathematical proof demonstrating that the line dividing a triangle from a vertex to the midpoint of its opposite side creates two triangles of equal area.

Craft a step-by-step proof, elucidating each geometric concept and confirming equal area conditions through reasoning.

8

How would you assess the impact of environmental changes on measuring land areas for agricultural crops? Discuss potential challenges in maintaining accurate area calculations.

Explore factors such as soil erosion or climate change, illustrating how these might affect land dimensions over time.

9

Analyze the significance of understanding area in urban planning. What challenges and opportunities exist when defining land usage based on area calculations?

Discuss how area measurement influences zoning regulations, building permits, and resource allocation in cities.

10

Propose and justify a simplification method to transform complex shapes into composite rectangles or triangles that facilitate easier area calculations.

Outline the approach and critically analyze its limitations and advantages when applied to various geometric forms.

Area Formula Sheet

Use this Class 8 Mathematics Area Formula Sheet for quick revision before school exams and CBSE exams. It brings together the important formulas, key concepts, and worked examples in one place so students can revise faster and download a printable PDF for offline study.

Important Formulas

1

Area of a Rectangle = Length × Width

The area (A) is the amount of space inside a rectangle. Length (l) is one side, and Width (w) is the adjacent side. This formula is essential for calculating the area in practical applications like flooring and landscaping.

2

Area of a Square = Side²

The area (A) of a square is calculated by squaring the length of one side (s). This is useful in determining the surface area of square plots or objects.

3

Area of a Triangle = 1/2 × Base × Height

Area (A) is calculated using the base (b) and height (h). This formula applies to any triangle and is fundamental in geometry, especially in construction and design.

4

Area of a Parallelogram = Base × Height

Area (A) is found by multiplying the base (b) with its corresponding height (h). This applies to various shapes in engineering and architecture.

5

Area of a Trapezium = 1/2 × (Base1 + Base2) × Height

Area (A) is determined by averaging the lengths of the two bases (b1, b2) and multiplying by the height (h). Useful in design and physical structures.

6

Area of a Circle = π × Radius²

Area (A) of a circle is calculated using π (approximately 3.14) and the radius (r). This is crucial in many applications including circular gardens and structures.

7

Area of a Sector = (θ/360) × π × Radius²

Area (A) of a sector of a circle is calculated based on the angle (θ) at the center. This is relevant in real-world problems involving circular arcs.

8

Area of an Ellipse = π × a × b

Area (A) for an ellipse is determined with a (semi-major axis) and b (semi-minor axis). This is applicable in fields such as astronomy and design.

9

Area of Composite Shapes = Sum of Areas of Individual Shapes

To find the area (A) of complex shapes, calculate and sum the areas of simpler components. This concept is widely applicable in construction and materials estimation.

10

Area of a Triangle with Two Sides and Included Angle = 1/2 × a × b × sin(C)

This formula calculates area (A) when two sides (a and b) and the included angle (C) are known. Useful in trigonometry and physics.

Worked Examples

1

A = l × w

Where A is the area, l is the length, and w is the width of the rectangle. This equation provides direct calculations for area.

2

A = s²

Where A is the area of the square and s is the length of one side. Directly useful when calculating multiple square areas.

3

A = 1/2 × b × h

Where A is the area of the triangle, b is the base, and h is the height. Essential for quick area calculations.

4

A = b × h

Where A is the area of the parallelogram. Useful in architecture and engineering applications.

5

A = 1/2 × (b1 + b2) × h

Where b1 and b2 are the lengths of the two bases of a trapezium, and h is the height. Important for calculations involving trapezoidal layouts.

6

A = π × r²

Where A is the area of a circle, and r is the radius. Fundamental in any context where circular objects or areas are involved.

7

A = (θ/360) × π × r²

This computes the area for a sector of a circle, crucial in engineering and design.

8

A = π × a × b

Where a is the semi-major and b is the semi-minor axis of an ellipse. Useful in various scientific applications.

9

A = A1 + A2 + ... + An

Sum of the areas of individual shapes making up a composite figure. This is critical in materials and design calculations.

10

A = 1/2 × a × b × sin(C)

Where a and b are two sides of a triangle, and C is the included angle. Important in trigonometric area calculations.

Explore More Area Resources

Explore more chapter resources to strengthen your understanding and prepare for exams.

Area Frequently Asked Questions

Learn how to calculate the area of various geometric shapes including rectangles, triangles, and polygons in Class 8 Mathematics. Explore practical applications and problem-solving techniques.

The area of a rectangle is calculated using the formula: Area = length × width. This means you multiply the length of the rectangle by its width to determine the total area it covers.
To find the area of a triangle, you can use the formula: Area = 1/2 × base × height. Measure the base and the height of the triangle, then apply these values to the formula.
Yes, it's possible for different shapes to have identical perimeters while having varying areas. For instance, a thin long rectangle and a square can share the same perimeter but have different areas.
To find the area, apply the formula: Area = length × width. Here, it would be 7 cm × 4 cm = 28 cm², so the area of the rectangle is 28 square centimeters.
The perimeter alone isn't a reliable measure of area because different shapes can have the same perimeter but differ in area. For example, two rectangles with the same perimeter can have different lengths and widths.
The area of a triangle can be seen as half of the area of a rectangle formed using the same base and height. Specifically, Area of triangle = 1/2 × Area of rectangle if the rectangle's base and height align with the triangle.
A unit square is a square with a side length of 1 cm. It is used to measure area, where the area of a larger shape can be determined by counting how many unit squares it contains.
Using the formula Area = 1/2 × base × height, the area would be 1/2 × 5 cm × 3 cm = 7.5 cm², thus the area of the triangle is 7.5 square centimeters.
To calculate the area of a polygon, you can divide it into simpler shapes, such as triangles or rectangles, calculate their areas separately, and then sum them for the total area of the polygon.
To find the area of a rectangle, you need two measurements: the length and the width. By multiplying these two dimensions, you will obtain the rectangle's area.
The concept of area is important in various real-world contexts, such as architecture, land measurement, and agriculture, where understanding the space covered by different shapes is essential for planning and design.
If the shape is regular (like a square), you can derive its dimensions from the perimeter. However, if it is irregular, additional measurements will be required to accurately compute the area.
If the base of a triangle is doubled while keeping the height constant, the area of the triangle will also double. This is due to the direct relationship between base length and area.
For complex shapes, you can use methods like decomposition (breaking the shape into simpler parts) or calculus for irregular shapes, incorporating formulas for areas known in geometry.
Yes, you can derive the area of a complex polygon by dividing it into non-overlapping triangles, calculating the area of each triangle, and then adding them together to find the total area.
Area represents the amount of two-dimensional space a shape covers, hence it is expressed in square units. For example, cm² indicates that the area is measured in terms of squares with sides of 1 cm.
Shapes such as squares and rectangles can be tiled perfectly without gaps or overlaps. Irregular shapes typically do not tile perfectly due to their unique dimensions.
To confirm if two rectangles have equal areas, calculate their areas using Area = length × width for both shapes and compare the results.
The area of a square is given by the formula Area = side × side. For a square with a side length of 6 cm, the area would be 6 cm × 6 cm = 36 cm².
Changing the dimensions of a rectangle will affect its area proportionally; increasing either length or width will increase the area, while decreasing them will reduce the area.
Yes, the areas of the triangles formed by dividing a rectangle using its diagonals are equal. Each diagonal divides the rectangle into two congruent triangles, sharing the same area.
The area of a trapezium can be calculated using the formula: Area = 1/2 × (base1 + base2) × height, where base1 and base2 are the lengths of the two parallel sides and height is the perpendicular distance between them.
To calculate the area of a circle, the formula is Area = π × radius². You can conceptually divide the circle into a series of triangles emanating from the center, but the formula is the standard approach.

Area PDF Downloads

Download worksheets, revision guides, formula sheets, and the official textbook PDF for Area.

Area Official Textbook PDF

Download the official NCERT/CBSE textbook PDF for Class 8 Mathematics.

Official PDFEnglish EditionNCERT Source

Area Revision Guide

Use this one-page guide to revise the most important ideas from Area.

Best for1-page chapter recap

Area Formula Sheet

Download the Area formula sheet PDF with important formulas, worked examples, and quick revision support for exam preparation.

Best forImportant formulas for quick revision

Area Practice Worksheet

Solve basic and application-based questions from Area.

Best forCore practice set

Area Mastery Worksheet

Work through mixed Area questions to improve accuracy and speed.

Best forMixed difficulty set

Area Challenge Worksheet

Try harder Area questions that test deeper understanding.

Best forFor deeper problem solving

Area Question Bank

Download important questions and exam-style prompts from Area.

Best forPrintable question set

Area Flashcards

Revise key terms and definitions from Area with interactive flashcards. Quick recall practice for CBSE Class 8 Mathematics.

These flash cards cover important concepts from Area in Ganita Prakash Part II for Class 8 (Mathematics).

1/19

What is the formula for the area of a rectangle?

1/19

Area of a rectangle = length × width. This formula calculates the total space within the rectangle.

How well did you know this?

Not at allPerfectly

2/19

How is area measured in square units?

2/19

Area is measured by counting the number of unit squares that fit inside the shape without overlaps.

How well did you know this?

Not at allPerfectly
Active

3/19

How can a square be divided into 4 equal areas?

Active

3/19

A square can be divided in infinitely many ways through different patterns such as drawing two perpendicular lines or by creative shapes maintaining equal area.

How well did you know this?

Not at allPerfectly

4/19

What is the formula for the area of a triangle?

4/19

Area of a triangle = 1/2 × base × height. This measures the space within the triangle.

5/19

What happens when a rectangle is divided by a diagonal?

5/19

A diagonal divides the rectangle into two congruent triangles, each having an area that is half of the rectangle's area.

6/19

Why can't perimeter be a measure of area?

6/19

Perimeter measures the boundary length, while area measures the space within. Different shapes can have the same perimeter but different areas.

7/19

How can the area of composite shapes be found?

7/19

The area of composite shapes is found by adding the areas of individual shapes that make it up.

8/19

What is the formula for the area of a circle?

8/19

Area of a circle = π × radius². It approximates the space within the circular boundary.

9/19

What does it mean to transform shapes into equal areas?

9/19

It involves rearranging or reshaping a figure to create a different shape that occupies the same amount of area.

10/19

What happens if the sidelength of a square is doubled?

10/19

The area increases by four times because area is proportional to the square of the length of the sides.

11/19

Can you give a real-world example of measuring area?

11/19

Calculating the lawn area for grass planting involves measuring length and width in meters and using the area formula.

12/19

Are the areas of triangles from a rectangle equal?

12/19

Yes, the triangles formed by drawing diagonals in a rectangle each have equal area.

13/19

How do you find the area of a path around a rectangle?

13/19

The area of the path can be calculated by subtracting the area of the inner rectangle from the area of the outer rectangle.

14/19

What information is needed to calculate a triangle's area?

14/19

You need the lengths of the base and height perpendicular to the base.

15/19

Do identical rectangles have the same area?

15/19

Yes, identical rectangles share the same dimensions, thus having the same area.

16/19

How to find area using midpoints of a triangle?

16/19

The area of a triangle formed by midpoints is equal to one-fourth of the area of the original triangle.

17/19

What is a fun activity to visualize area?

17/19

Dividing a square into four parts and rearranging them to form a new shape underscore principles of area.

18/19

What is a common mistake in calculating areas?

18/19

Assuming all shapes with the same perimeter also have the same area can lead to incorrect conclusions.

19/19

Which triangle has maximum area with a common base?

19/19

The triangle with the vertex directly above the base will have the maximum area.

View all 19 Area flashcards

Practice Area with Interactive Duels

Live Academic Duel

Master Area via Live Academic Duels

Challenge your classmates or test your individual retention on the core concepts of CBSE Class 8 Mathematics (Ganita Prakash Part II). Compete in speed-recall question rounds matched explicitly to the latest syllabus milestones for Area.

CBSE-aligned questions
Instant speed-recall rounds

Quick, competitive practice on Area with zero setup.