Question

Find the area and the perimeter of the shaded portion in the adoining figure:

Answer 1

Area of the shaded region $=$area of the semicircle with diameter AD+area of the semicircle with diameter EC+area of the semicircle with diameter BC-area of the semicircle with diameter AB- area of the semicircle with diameter DE

$=(\frac{22}{7}\times 7\times 7\times \frac{1}{2})-(\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{1}{2})+(\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\times \frac{1}{2})-(\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{1}{2})+(\frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}\times \frac{1}{2})$

$=77+173.25-19.25$

$=231c{m}^2$

Perimeter of the shaded region $=$perimeter of the semicircle with diameter AB+perimeter of the semicircle with diameter AD+perimeter of the semicircle with diameter BC+perimeter of the semicircle with diameter DE+perimeter of the semicircle with diameter EC

$=\frac{22}{7}\times \frac{7}{2}+\frac{22}{7}\times 7+\frac{22}{7}\times \frac{21}{2}+\frac{22}{7}\times \frac{7}{2}+\frac{22}{7}\times \frac{7}{2}$

$=88cm$