Question

In the given figure a square OABC is inscribed in a quadrant OPBQ. If OA =20cm, find the area of the shaded region.

Answer 1

Area of shaded region = Area of quadrant OBPQ – Area of square OABC

Area of square OABC

Given: Side of square = 20cm

Area of square = Side × Side

= 20 × 20

= 400 cm²

Area of quadrant

We need to find the radius

Joining OB

Also, all angles of a square are 90°

∴∠BAO = 90°

Hence, ΔOBA is a right triangle

In ΔOBA, by Pythagoras Theorem

(Hypotenuse)² = (Perpendicular)² + (Base)²

(OB)² = (AB)² + (OA)²

⇒ (OB)² = (20)² + (20)²

⇒ (OB)² = 400 + 400

⇒ (OB)² = 800

⇒ OB = √(10×10×2×2×2)

⇒ OB = 20√2cm

= 628 cm²

Area of shaded region = Area of quadrant OBPQ – Area of square OABC

= 628 – 400

= 228cm²