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

For ΔABC,

AC² = AB² + BC²

(5)² = (3)² + (4)²

Therefore, ΔABC is a right-angled triangle, right-angled at point B.

Area of ΔABC = 1/2 x AB x BC = 1/2 X 3 X 4 = 6CM²

For ΔADC,

Perimeter = 2s = AC + CD + DA = (5 + 4 + 5) cm = 14 cm

s = 7 cm

By Heron’s formula,

Area of ABCD = Area of ΔABC + Area of ΔACD

= (6 + 9.166) cm² = 15.166 cm² = 15.2 cm2 (approximately)