Area of Quadrilateral

The area of a quadrilateral is the total space enclosed within the quadrilateral.

As we know quadrilateral is any shape having four different sides, it does not have a common formula for all its shapes. However we can derive a general formula for determining the area of any quadrilateral by using the following procedure.

How to Find the Area of a Quadrilateral

To determine the area of a quadrilateral, we need to divide the quadrilateral into two triangles. Finding the area of both the triangles and adding them will give us the area of the quadrilateral.

Following the above procedure, let us determine the formula for area of quadrilateral ABCD.

Given is a quadrilateral ABCD, whose diagonal BD = 20 cm and the height of ∆ABD = 8 cm and ∆CBD = 6 cm. Find the area of the quadrilateral ABCD.

Solution:

As we know, A = ½ x d x (h₁ + h₂), here d = 20 cm, h₁= 8 cm, and h₂ = 6 cm
 = ½ x 20 x (8 + 6) cm²
 = ½ x 20 x 14 cm²
 = 140 cm²

Calculate the area of the quadrilateral PQRS, whose diagonal is 10 m and the heights of ∆PQS and ∆RQS, are 5.5 m and 6.5 m respectively.

Solution:

As we know, A = ½ x d x (h₁ + h₂), here d = 10 m, h₁ = 5.5 m, and h₂ = 6.5 m
= ½ x 10 x (5.5 + 6.5) m²
= ½ x 10 x 12 m²
= 60 m²

Area of Special Quadrilaterals

By using the above formula we can calculate the area of any quadrilateral.

If we are looking to find the area of special quadrilaterals such as rectangle, square, parallelogram, rhombus, trapezoid, and kite, then we can use the formulas given below.