Q12 of 46 Page 1

In Fig. 6, OABC is a square of side 7 cm. If OAPC is a quadrant of a circle with centre O, then find the area of the shaded region.

Given: OC = CB = BA = AO = 7 cm

To find: Area of the shaded area, which implies Area of CBAP.



We can formulate a formula to find the area of the shaded region, CBAP.


Let OC = CB = BA = AO = r as side of square = radius of quadrant.


As


Area of square CBAO = Area of quadrant of the circle OCPA + Area of shaded region CBAP


⇒ Area of shaded region CBAP = Area of square CBAO – Area of quadrant of the circle OCPA


⇒ Area of shaded region CBAP = (r)2– [πr2]/4


[∵, Area of square = (side)2 = (r)2 and area of quadrant of circle = (πr2)/4]


⇒ Area of shaded region CBAP = (7)2 – [3.14×(7)2]/4 = 49 – 38.46 = 10.5


Hence, area of shaded region is 10.5 cm2


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