Question

1) Do both shaded and unshaded portions have equal area or not?

2) A student said both the boundaries have same length in the diagram. Is s/he right?

3)what is the area of the shaded region

4) what is the length of the boundary of the unshaded region?

5) what is the circumference and area of the whole diagram?

​

Answer 1

$\bold{ANSWER≈}$

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