Q. 134.6( 7 Votes )

# In Fig. 2, a squa

Answer :

Construction: Join OB.

Let us consider ΔAOB,

By Pythagoras Theorem,

OB2 = OA2 + AB2

Given, side of square OA = 20 cm.

OB2 = 202 + 202

OB2 = 800

OB = 20√2 cm

Thus, radius of circle, r = 20√2 cm

We know that area of quadrant = (θπr2)/360°

So, area of quadrant OQBP = (90° × π × (20√2)2)/360°

= 200 × 3.14

= 628 cm2

We know that area of square = (side)2

So, area of square OABC = (20)2

= 400 cm2

Thus, area of Shaded region = Area of Quadrant OQBP – Area of square OABC

= (628 – 400) cm2

= 228 cm2

Ans. The area of shaded region is 228 cm2.

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