Q31 of 37 Page 13

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


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


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