Question

In fig. ABCD is a rectangle with AB= 14 cm and BC= 7 cm. Taking DC, BCand AD as diameter, three semicircles are drawn. Find the area of the shaded portion.

Answer 1

Given:
Length of a rectangle (AB) = DC = 14 cm
Breadth of a rectangle( BC) = AD=7 cm

AREA OF SEMICIRCLE with DIAMETER DC= 1/2πr² = ½(22/7) × (14/2)²
= 11 × 7 = 77 cm²

AREA OF RECTANGLE (ABCD) = Length × Breadth = AB × DC = 14 × 7 = 98 cm²

AREA OF 2 SEMI CIRCLE with DIAMETER BC & AD= 2× 1/2πr² =(22/7) × (7/2)² = 11 ×7 / 2
= 77 /2 cm²

AREA OF SHADED REGION = Area of rectangle ABCD -  area of semicircle with diameter DC + Area of 2 semicircle with diameter  BC and AD

Area of shaded region = 98 - 77 + 77/2
= 21 +  77/2 = (42 +77)/2 = 119/2 = 59.5 cm²
Area of shaded region = 59.5 cm²

Hence, the Area of shaded region is 59.5 cm².

HOPE THIS WILL HELP YOU..

Answer 2

refer to the attached ANS
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