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 region. ${\displaystyle [User=\frac{22}{7}]}$

Answer 1

It is given that OABC is a square of side 7 cm.

∴ Area of square OABC = (7)² cm² = 49 cm²

Also, it is given that OAPC is a quadrant of circle with centre O.

∴Radius of the quadrant of the circle = OA = 7 cm

∴ Area of the quadrant of circle ${\displaystyle \frac{1}{4}\left({\pi }^2\right)}$

${\displaystyle =\frac{1}{4}(\pi \times 7^2)c{m}^2}$

${\displaystyle =\frac{49\pi }{4}c{m}^2}$

${\displaystyle =\frac{49}{4}\times \frac{22}{7}c{m}^2}$

${\displaystyle =\frac{77}{2}c{m}^2}$

∴Area of the shaded region = Area of Square − Area of Quadrant of circle.

${\displaystyle =[49-\frac{77}{2}]c{m}^2}$

${\displaystyle =\left[\frac{98-77}{2}\right]c{m}^2}$

${\displaystyle =\frac{21}{2}c{m}^2}$

${\displaystyle =10.5c{m}^2}$

Thus, the area of the shaded region is 10.5 cm².