Question

Find the area of shaded region in each of the following figures

Answer 1

(i) Area of the shaded region
$=\left\{\text{Area of the square with side}21m\right\}-\left\{\text{Area of the circle with diameter}21m\right\}$
If the diameter of the circle is $21m$
Then the radius of the circle $=\frac{22}{5}=10.5m$
Area of the shaded region $=(21\times 21)=(\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2})m^2$
$=441-346.5$
$=94.5m^2$
(ii) Area of shaded region $=\left\{\text{Area of the square with side}21m\right\}-\{4\times \text{Area of the sector}\}$
$=(21-21)-(4\times \frac{{90}^{\circ }}{{360}^{\circ }}\times \frac{22}{2}\times \frac{21}{2}\times \frac{21}{2})m^2$$
(if diameter is $21m$, then radius is $\frac{21}{2}m$)
$=(21\times 21)=(4-\frac{1}{4}\times \frac{22}{7}\times \frac{21}{2}\times \frac{21}{2})$
$=(441-346.5)m^2$
$=94.5m^2$