Question

Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Answer 1

Here, we are given sides of a quadrilateral ABCD as

AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

Here, we see that AB² + BC² = AC²

i e. (3)² + (4)² = (5)²

Hence, ∆ABC is right angled at B

= √(7 x 2 x 2 x 3)

= 2√21 cm²

Hence, area of quadrilateral ABCD 

= ar (∆ABC) + ar (∆ACD) 

= (6 + 2√21) cm²