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

In the right angled ACB :

AB² = BC² + AC²

\(\Rightarrow\) 17² = BC² + 15

\(\Rightarrow\) 17² - 15² = BC²

\(\Rightarrow\) 64 = BC²

\(\Rightarrow\) BC = 8 cm

Perimeter = AB + BC + CD + AD

= 17 + 8 + 12 + 9

= 46 cm

∴ Area of the quadrilateral = Area of \(\triangle ABC\) + Area of \(\triangle ADC\)

= 60 + 54

= 114 cm²