Question

Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.

Answer 1

The quadrilateral ABCD having sides AB,BC,CD,DA and diagonal BD is given, where BD divides ABCD into two triangles

ΔDBC and ΔDAB

In triangle DBC, we can observe that

DC² = DB² + BC²

Therefore, it is a right angled triangle.

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

Where,

Base = BC = 21 cm; Height = BD = 20 cm

Area of triangle DAB, say A₂ having sides a, b, c and s as semi-perimeter is given by

, where

a = DB = 20 cm; b = AD = 34 cm; c = AB = 42 cm

Area of quadrilateral ABCD, say A

A = Area of triangle DBC + Area of triangle DAB