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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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Academic Mathematics NCERT Class 10

Given: Diameter of small semi-circles$=3\ cm$. Diameter of larger semi-circle$=4.5\ cm$ and radius of the circle$=4.5\ cm$.

To do: To find the area of the shaded region.

Solution:

Radius of small semi-circle$=\frac{Diameter}{2} =\frac{3}{2} \ cm$

radius of larger semi-circle$=4.5\ cm\ =\frac{9}{2}\ cm$

radius of the circle$=4.5cm\ =\frac{9}{2} \ cm$

Area of the shaded region $=$

[Area of the larger semi-circle]$-$[Area of the circle]$-2$[Area of the two small semi cirle$+$area of one small semi circle]

$=\frac{\pi }{2}\left(\frac{9}{2}\right)^{2} -\frac{\pi }{2}\left(\frac{9}{2}\right)^{2} -2\times$

Area of shaded region $=12.36\ cm$

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Updated on: 10-Oct-2022

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