Question

Given that the curves are formed from quarter circles,
find the area of the shaded region.
Give your answer in terms of π
.

Answer 1

Given : curves are formed from quarter circles

To Find : area of the shaded region.

Solution:

area of the shaded region.  = area of both Quarter circle - area of  Square

= 2 * area of one Quarter circle - area of  Square

area of one Quarter circle = ( 1/4)π(12)²   = 36π  m²

area of  Square = 12 * 12 = 144 m²

area of the shaded region.  = 2 * 36π - 144 m²

= 72π - 144  m²

= 72 (π - 2)   m²

area of the shaded region   =  72 (π - 2)   m²

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