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Question
In Fig. 4, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region.
(use `pi=22/7`)
Solution
Let the four shaded regions be I, II, III and IV and the centres of the semicircles be P, Q, R and S, as shown in the figure.
It is given that the side of the square is 14 cm.
Now,
Area of region I + Area of region III = Area of the square − Areas of the semicircles with centres S and Q
=14×14−2×`1/2`×π×72 (∵ Radius of the semicircle=7 cm)
`=192-49xx22/7`
=196−154
=42 cm2
Similarly,
Area of region II + Area of region IV = Area of the square − Areas of the semicircles with centres P and R.
=14×14−2×`1/2`×π×72 (∵ Radius of the semicircle=7 cm)
=196−49×`22/7`
=196−154
=42 cm2
Thus,
Area of the shaded region = Area of region I + Area of region III + Area of region II + Area of region IV
= 42 cm2 + 42 cm2
= 84 cm2
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