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.

Answer 1

Area of shaded region

Area of semi-circle PQR = $\frac{1}{2}\pi (\frac{9}{2}{)}^2$

=$\frac{81\pi }{8}c{m}^2$

Area of region circle, A = $\pi (\frac{9}{4}{)}^2$

= $\frac{81\pi }{16}c{m}^2$

Area of region (B + C) = $\pi (\frac{3}{2}{)}^2$

= $\frac{9\pi }{4}c{m}^2$

Area of region D = $\frac{1}{2}\pi (\frac{3}{2}{)}^2$

= $\frac{9\pi }{8}c{m}^2$

Area of shaded region = Area of the semicircle PQR - Area of circle A - Area of the region (B + C) + Area of region D

= $\frac{81\pi }{8}c{m}^2$ - $\frac{81\pi }{16}c{m}^2$ -$\frac{9\pi }{4}c{m}^2$ + $\frac{9\pi }{8}c{m}^2$

= $\frac{63\pi }{16}c{m}^2$

= $\frac{99}{8}c{m}^2$

= 12.37 cm²