Quadrilaterals – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash Part I, tailored for Class 8 in Mathematics.
This one-pager compiles key formulas and equations from the Quadrilaterals chapter of Ganita Prakash Part I. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
Sum of angles in a quadrilateral: ∠1 + ∠2 + ∠3 + ∠4 = 360°
This formula states that the sum of all internal angles in any quadrilateral is always 360°. This property is fundamental in solving problems involving quadrilaterals.
Area of a rectangle: A = l × w
A represents the area, l is the length, and w is the width. This formula is vital in real-world applications such as calculating land area.
Area of a square: A = s²
A is the area and s is the side length. Useful for determining the area of any square, helping in tasks like flooring calculations.
Perimeter of a rectangle: P = 2(l + w)
P represents the perimeter, l is the length, and w is the width. Important for applications involving fencing around a rectangular plot.
Perimeter of a square: P = 4s
P is the perimeter of the square with side length s. This formula is straightforward and frequently applied in geometric problems.
Diagonal of a rectangle: d = √(l² + w²)
d represents the length of the diagonal. This formula is derived from the Pythagorean theorem and is used in construction to ensure right angles.
Properties of a rectangle: Opposite sides are equal (AB = CD and AD = BC)
This property helps in identifying rectangles by verifying side lengths during construction or problem-solving.
Properties of a square: All sides equal and diagonals bisect at 90°
This defines how squares can be easily recognized and constructed, ensuring that all properties are met.
Properties of a parallelogram: Opposite sides are equal (AB = CD) and adjacent angles are supplementary (∠A + ∠B = 180°)
Fundamental in understanding the relationships between sides and angles in parallelograms.
Diagonal of a rhombus: d = √(s² + s²) = s√2
s is the side length of the rhombus. This formula demonstrates how to calculate the diagonal length based on side length.
Equations
∠A + ∠B + ∠C + ∠D = 360°
Indicates the sum of angles in a quadrilateral. Essential for proving angle relationships in geometric problems.
l² + w² = d² (For rectangles)
This comes from the Pythagorean theorem relating to calculating the diagonal of a rectangle, crucial for geometrical design.
AB || CD and AD || BC (for rectangles)
Indicates that both pairs of opposite sides are parallel, vital in classifying quadrilaterals.
Area of parallelogram: A = b × h
Where b is the base length and h is the height. This is used for problems involving the area of parallelograms in real life.
Area of kite: A = (p₁ × p₂) / 2
Where p₁ and p₂ are the lengths of the diagonals. Important for deriving the area of kites in geometric applications.
2AB + 2BC = P (perimeter of a parallelogram)
Shows how to compute the perimeter based on the lengths of two adjacent sides.
AB = CD (for parallelogram)
Establishes that opposite sides of a parallelogram are equal, a core property in quadrilaterals.
AD = BC (for parallelogram)
Equates opposite sides to confirm the structure of a parallelogram.
AB = CD = s (in rhombus)
Defines that all sides in a rhombus are equal, crucial for identifying rhombuses.
d₁ = d₂ (diagonals of a rhombus)
The lengths of the diagonals in a rhombus are equal, a property used in classifying geometric shapes.
