Question

Find the perimeter of the given figure which involves four semicircle s each drawn on a side of a square of side 14 cm.

Answer 1

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

=14×14−2×1212×π×72          (∵ Radius of the semicircle=7 cm)

=192−49×227=192-49×227

=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.

=14×14−2×1212×π×72    (∵ Radius of the semicircle=7 cm)

=196−49×227227

 =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