Q. 164.0( 222 Votes )

Calculate the area of the designed region in Fig. 12.34 common between the two quadrants of circles of radius 8 cm each

Answer :

First, let us understand how we can acquire the given Area
From the figure first we need to subtract Area of quadrant from the square and then again subtract another quadrant from the square, by this, we will get the Area of the unshaded region
And finally to find Area of the shaded region we can subtract Area of the unshaded region from Area of square.
Radius of quadrant = length of square
= r
= 8 cm
We can interpret from above that:
Area of unshaded region = 2(Area of the square - Area of the quadrant of the circle)
Area of shaded region = Area of square - 2(Area of square - Area of quadrant of circle)

Area of shaded region = 2 (Area of quadrant of circle) - Area of square

 = 2 × (1/4)πr2 -   8 × 8

 = [(1/2) × π × 82] - 64

 = 32π - 64

 = 32(π-2)

 = 32 × 1.14

 = 36.54 cm2

Therefore, area of shaded region is 36.54 cm2

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