Question

In figure, $OABC$ is a square of side $7cm.$ If $OAPC$ is a quadrant of a circle with centre $O,$ then find the area of the shaded region. $[Use\pi =\frac{22}{7}].$

Answer 1

Given that OABC is a square of side $7cm.$
Therefore, Area of square $OABC=(7{)}^{2}c{m}^2=49c{m}^2$
Also, it is given that OAPC is a quadrant of circle with centre O.
Radius of the quadrant of the circle $=OA=7cm$
Therefore, Area of the quadrant of circle $=\frac{1}{4}\left(\pi r^2\right)$
$=\frac{1}{4}(\pi \times 7^2)$
$=\frac{49\pi }{4}$
$=\frac{49\times 22}{4\times 7}$
$=\frac{77}{2}$ $c{m}^2$
Therefore, Area of the shaded region $=$ Area of Square − Area of Quadrant of circle.
$=49-\frac{77}{2}$
$=\frac{98-77}{2}$
$=\frac{21}{2}$

$\Rightarrow 10.5$ $c{m}^2$
So, the area of the shaded region is $10.5c{m}^2$