Question

In fig. 3, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Answer 1

Let us join OB.

In ΔOAB:
OB² = OA² + AB²  = (20)² + (20)² = 2 ×  (20)²

⇒ OB = 20 √2

Radius of the circle, r = `20 sqrt2` cm

`"Area of qudrant OBPQ"=90^@/360^@xx3.14xx(20sqrt2)^2`

`=90/360xx3.14xx(20sqrt2)^2 cm^2`

`=1/4xx3.14xx800 cm^2`

`=628 cm^2`

Area of square OABC = (Side)² = (20)² cm² = 400 cm²

∴ Area of the shaded region = Area of quadrant OPBQ − Area of square OA

                                             = (628 − 400) cm²

                                             = 228 cm²