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. `[\text\ User=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 `1/4(pi^2)`

`=1/4(pixx7^2)cm^2`

`=(49pi)/4cm^2`

`=49/4xx22/7 cm^2`

`=77/2cm^2`

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

`=[49-77/2]cm^2`

`=[(98-77)/2]cm^2`

`=21/2cm^2`

`=10.5cm^2`

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