Q29 of 49 Page 1

Find the area of the shaded region in Fig. 7, where arcs are drawn with centers 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, where the length of each side of the square is 14 cm.

P, Q, R, S are the midpoints of the AB, BC, CD, and DA respectively.

AP=1/2 AB=1/2(14)=7cm


r=7cm


As the radius of all quadrants is same, the area of all the 4 quadrants will also be same.


Area of shaded region= Area(square) – 4 × Area(quadrant)


=


=


= 196-154 =42cm2


∴ Area of the shaded region is 42cm2


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