Question

answer this.........

Answer 1

Answer:

AREA OF BIG  SEMICRICLE ==> 1/2 * 22/7 * 3*3 ==>  11*3*3/7 ==> 99/7

AREA OF SMALL SEMI CIRCLE ==> 1/2*22/7*1.5*1.5 ==> 11*15*15/7*10*10

   ===> 11*3*3 / 7*2*2 ==> 99/28

AREA OF SMALL CIRCLE ==> 22/7 * 15/10*15/10 ==> 198/28

AREA OF SHADED REGION = AREA OF BIG SEMICIRCLE+AREA OF SMALL SEMICIRCLE  - 2(AREA OF SMALL SEMICIRCLE ) - AREA OF CIRCLE

AREA OF SHADED REGION ==> 99/7 + 99/28 -  2(99/28) - 198/28

AREA OF SHADED REGION ==> 99/7 +  99/28 - 198/28 - 198/28

AREA OF SHADED REGION = 99/7 - 99/28 - 198/28

AREA OF SHADED REGION ==> 99/7-297/28

AREA ==>  396-297/28

AREA ==> 99/28

Answer 2

Let's say the larger semicircle is area A, the circle is area 1, and the three smaller semicircles as area 2,3 and 4.

We need to find the shaded region.

Shaded area = Area A - area 1 - area 2 - area 3 + area 4 (Any doubt in this?)

_____________
● Area A:

Larger semicircle has radius = 9/2 = 4.5cm

Area A = area of larger semicircle = (πR^2)/2 = (π × (9/2)^2) / 2 = 81π/8 cm^2

● Area 1

The circle has diameter = radius of larger semicircle = 9/2 cm

radius = 9/4 cm

Area of circle(Area 1) = πr^2 = π × (9/4)^2 = 81π/16 cm^2

● Area 2, 3 and 4 are semicircles with diameter 3cm

radius = 3/2 cm

Area (2,3,4) = (πr^2)/2 = (π × (3/2)^2)/2 =9π/8 cm^2
_________________________

Shaded area = Area A - area 1 - area 2 - area 3 + area 4

= 81π/8 - 81π/16 - 9π/8 - 9π/8 + 9π/8

= 81π/8 - 81π/16 - 9π/8

Take LCM = 16

= (162π - 81π - 18π) / 16

= 63π/16

= 63/16 × 22/7

= 99/8 cm^2

= 12.375 cm^2

Area of Shaded region is 12.375 cm^2.