Question

In the adjoining diagram , ABC ,CDE and AFE are three semicircles. IF AC = CE = 7 cm, Find the area of shaded portion.​

Answer 1

Answer:

38.5 cm

Step-by-step explanation:

Since AC = CE = 7cm, radius of AFE = 7cm

Area of semi circle AFE =

$= \frac{1}{2} \times \frac{22}{7} \times 7 {}^{2}$

$= \frac{1}{2} \times \frac{22}{7} \times 49$

$= \frac{1}{2} \times 22 \times 7$

$= 11 \times 7$

$= 77cm$

Area of Semi circle ABC

Diameter = 7cm , Radius = 7/2

$\frac{1}{2} \times \frac{22}{7} \times (\frac{7}{2})^{2}$

$\frac{1}{2} \times \frac{22}{7} \times \frac{49}{4}$

$= \frac{1078}{56}$

$= 19.25cm$

Since AC = CE

Semi circle ABC and Semi circle CDE share same radius.

Hence Area ABC = Area CDE

Area of CDE = 19.25

Area of shaded region = Area of AFE - ( Area of ABC + Area of CDE)

Area of shaded region = 77 - ( 19.25 + 19.25)

= 77 - 38.5

= 38.5

Area of shaded region = 38.5 cm