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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