Question

Find the perimeter and area of the quadrilateral ABCD in which AB = 17 cm, AD = 9 cm, CD = 12 cm, ∠ACB = 90° and AC = 15 cm.

Answer 1

We assume ABCD be the quadrilateral having sides AB, BC, CD, DA and ∠ACB = 90^∘.

We take a diagonal AC, where AC divides ABCD into two triangles ΔACB and ΔADC

Since ∆ACB is right angled at C, we have

AC = 15 cm; AB = 17 cm

AB² = AC² + BC²

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

, where,

Base = BC = 8 cm; Height = AC = 15 cm

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

, where

a = AD = 9 cm; b = DC = 12 cm; c = AC = 15 cm

Area of quadrilateral ABCD, say A

A = Area of ∆ACB + Area of ∆ADC

Perimeter of quadrilateral ABCD, say P