Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use π = 3.14]

 

Answer

The area formed by the four quadrants is equal to the area of a circle. So, you have to subtract the area of a circle from the area of the square.

Radius of each arc drawn = 6 cm

Area of four quadrants or area of circle = πr2

= 3.14 × 6 × 6

= 113.04 cm2

Area of square ABCD = a2

= 12 × 12 = 144 cm2

Hence, area of shaded region = 144 - 113.04

= 30.96 cm2

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