Question

In the figure, 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.​

Answer 1

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Answer 2

Answer:

84cm²

Step-by-step explanation:

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)

=192-49×22/7

=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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