Question

The shaded area below is the common area to four semicircles whose diameters are sides of the
square with side length 8.
If the area of the shaded region is A, then the least integer greater than Ais​

Answer 1

Answer:

1. Length of the boundary

Length of the boundary=perimeter of semi circle with diameter AB boundary of semi circle with diameter 7cm

Length of boundary =(π×7+π×3.5)+π×1.75+π×1.75

Length of boundary =π(7+3.5+1.75+1.75)

=44cm

∴ The length of the boundary is 44cm.

2.Area of shaded region =

Area of largest semicircle + Area of medium semicircle-2 (Area of small semicircle )

Area=

7

22

×

2

7×7

+

7

22

×

100

35

×

2

35

−2(

7

22

−

100×100

175×175

)

=77+19.25−2(481)

=96.25−9.62

=86.63cm

2

Area of shaded region =86.63cm

2