Area – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash Part II, tailored for Class 8 in Mathematics.
This one-pager compiles key formulas and equations from the Area chapter of Ganita Prakash Part II. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Equations
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.
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.
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.
A = b × h
Where A is the area of the parallelogram. Useful in architecture and engineering applications.
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.
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.
A = (θ/360) × π × r²
This computes the area for a sector of a circle, crucial in engineering and design.
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.
A = A1 + A2 + ... + An
Sum of the areas of individual shapes making up a composite figure. This is critical in materials and design calculations.
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.
