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Question

Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region.
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Solution

Area of big semicircle =12πr2=π2×(4.5)2

Area of one small semicircle =π2×(1510)2

Area of the given figure =π2[45×45100+15×15100]=45π4cm2

Area of circle =π×(4510)2

Area of the shaded region = Area of a given figure - Area of circle 2× Area of small semicircles

=45π445×45π100×42×π2(15×15100)

=45π100×[2511.255]

=45×22100×7×8.75

Area of the shaded region=12.375cm2

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