Question

ABCD is a rectangle, AB = 15 cm, AC = 17 cm. Find the area of parallelogram PQCA.

Answer 1

Given:

• Rectangle ABCD
• AB = 15 cm
• AC = 17 cm (diagonal of rectangle)

Find: Area of parallelogram PQCA

Since ABCD is a rectangle:

AC² = AB² + BC²

17² = 15² + BC²

289 = 225 + BC²

BC² = 289 − 225 = 64

BC = 8 cm

So rectangle dimensions are 15 cm × 8 cm

Area of ABCD = AB × BC = 15 × 8 = 120 cm²

Diagonal AC divides rectangle ABCD into two equal triangles of area `1/2 xx 120 = 60` cm².

Parallelogram PQCA is constructed such that its area = twice the area of △ABC

So: 

Area of PQCA = 2 × Area of △ABC

Now, △ABC is a right-angled triangle:

Area of △ABC = `1/2 xx AB xx BC`

= `1/2 xx 15 xx 8 = 60` cm²

Area of PQCA = 2 × 60 = 120 cm²