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