Answer :

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 cm^{2}

**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 cm^{2}

Area of shaded region = Area of quadrant OBPQ

– Area of square OABC

= 628 – 400

= 228cm^{2}

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