Question

In the given figure.APB and CQD are semicircles of diameters 7$cm$ each. White ARC and BSD are semicircles of diameters 14$cm$ each find the perimeter and area of the shaded region. $(\pi =\frac{22}{7})$

Answer 1

The radius of semi circle $ARC$ is $7cm$

The radius of semi circle $APis$3.5cm

The perimeter of curve is given as $ARC+CQD+DSB+APB\frac{22}{7}\times 7+\frac{22}{7}\times 3.5+\frac{22}{7}\times 3.5+\frac{22}{7}\times 7\frac{22}{7}\left(21\right)=66cm$

The area is given as $ar\left(ARC\right)-ar\left(APB\right)+ar\left(BSD\right)-ar\left(CQD\right)\frac{22}{7}\times 7^2-\frac{22}{7}\times {3.5}^2+\frac{22}{7}\times 7^2-\frac{22}{7}\times {3.5}^2\frac{22}{7}\times (49+49-12.25-12.25)=\frac{22}{7}\times 73.522\times 10.5=231c{m}^2$