Question

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

Answer 1

Area of big semicircle $=\frac{1}{2}\pi r^2=\frac{\pi }{2}\times (4.5{)}^2$

Area of one small semicircle $=\frac{\pi }{2}\times {\left(\frac{15}{10}\right)}^2$

Area of the given figure $=\frac{\pi }{2}[\frac{45\times 45}{100}+\frac{15\times 15}{100}]=\frac{45\pi }{4}c{m}^2$

Area of circle $=\pi \times {\left(\frac{45}{10}\right)}^2$

Area of the shaded region $=$ Area of a given figure - Area of circle $-2\times$ Area of small semicircles

$=\frac{45\pi }{4}-\frac{45\times 45\pi }{100\times 4}-2\times \frac{\pi }{2}\left(\frac{15\times 15}{100}\right)$

$=\frac{45\pi }{100}\times [25-11.25-5]$

$=\frac{45\times 22}{100\times 7}\times 8.75$

Area of the shaded region$=12.375c{m}^2$