Question

In Fig.6, OABC is a square of side 7 cm. IF OAPC is a quadrant of a circle with centre O, then find the area of the shaded regions. [Use =$\frac{22}{7}$]

Answer 1

It is given that OABC is a square of side 7 cm.
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.
$\therefore$ Radius of the quadrant of the circle = OA =7 cm
$\therefore$ Area of the quadrant of circle =$\frac{1}{4}\left(\pi r^2\right)$
$=\frac{1}{4}(\pi \ast 7^2)c{m}^2=\frac{49\pi }{4}c{m}^2=\frac{49}{4}\times \frac{22}{7}c{m}^2=\frac{77}{2}c{m}^2$
$\therefore$ Area of the shaded region =Area of Square -Area of Quadrant of circle
$=[49-\frac{77}{2}]c{m}^2=\left[\frac{98-77}{2}\right]c{m}^2=\frac{21}{2}c{m}^2=10.5c{m}^2$
Thus, the area of the shaded region is $10.5c{m}^2$.