Question

A sheet of paper is in the form of rectangle ABCD in which AB = 40cm and AD = 28 cm. A semicircular portion with BC as diameter is cut off. Find the area of remaining paper.

Answer 1

Given sheet of paper ABCD

AB = 40 cm, AD = 28 cm

⇒ CD = 40 cm, BC = 28 cm [since ABCD is rectangle]

Semicircle be represented as BMC with BC as diameter

Radius =`1/2` × 𝐵𝐶 = `1/2 × 28 = 14`𝑐𝑚𝑠

Area of remaining (shaded region) = (area of rectangle) – (area of semicircle)

= (𝐴𝐵 × 𝐵𝐶) − (`1/2` 𝜋𝑟2)

= (40 × 28) −` (1/7×22/7× 14 × 14)`

= 1120 − 308

= 812 cm².