In the figure (i) given below, ABCD is a rectangle, AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded portion.
Mensuration
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Question

In the figure (i) given below, ABCD is a rectangle, AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded portion.

Mensuration

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KnowledgeBoat · Accepted Answer

Since, ABCD is a rectangle. AD = BC = 7 cm. CD = AB = 14 cm. From figure, AD and BC are diameters of smaller circles. Radius = = 3.5 cm. Area of each small semi-circle = = = 19.25 cm². From figure, CD is the diameter of the larger semi-circle. Radius = = 7 cm. Area of larger semi-circle = = = 77 cm². Area of rectangle ABCD = AB × BC = 14 × 7 = 98 cm². From figure, Area of shaded region = Area of rectangle ABCD + 2 × Area of each smaller semi-circle - Area of larger semi-circle = 98 + (2 × 19.25) - 77 = 98 + 38.5 - 77 = 59.5 cm². Hence, area of shaded region = 59.5 cm².

Mathematics

In the figure (i) given below, ABCD is a rectangle, AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded portion.

Mensuration

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