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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.
Solution
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` × ๐ต๐ถ = `1/2 × 28 = 14`๐๐๐
Area of remaining (shaded region) = (area of rectangle) – (area of semicircle)
= (๐ด๐ต × ๐ต๐ถ) − (`1/2` ๐๐2)
= (40 × 28) −` (1/7×22/7× 14 × 14)`
= 1120 − 308
= 812 cm2.
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