Find the area of a quadrilateral ABCD in which AD = 24 cm, ∠BAD = 90° and BCD forms an equilateral triangle whose each side is equal to 26 cm.

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Solution

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA, diagonal BD and angle where BCD forms an equilateral triangle having equal sides.

We need to find area of ABCD

In triangle BAD, we have

BD² = BA²+ AD².So

Area of right angled triangle ABD, say A₁ is given by

Where,

Base = BA = 10 cm; Height = AD = 24 cm

Area of equilateral triangle BCD, say A₂having sides a, b, c is given by

, where

a = BC = CD = BD = 26 cm

Area of quadrilateral ABCD, say A

A = Area of triangle BAD + Area of triangle BCD

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