Question

Find the area of shaded region of the figure given below

Answer 1

Shaded area $=$ Area $ADBCLA+$ Area $EFGE+$ Area $BEGKCB$

$=\frac{1}{2}\times \pi [{\left(\frac{10.5}{2}\right)}^2-{\left(\frac{7}{2}\right)}^2]+\frac{1}{2}\pi {\left(\frac{7}{2}\right)}^2+\frac{1}{2}\pi [{\left(\frac{17.5}{2}\right)}^2-{\left(\frac{7}{2}\right)}^2]c{m}^2$

$=(\frac{1}{2}\times \frac{22}{7}\times \frac{35}{4}\times \frac{7}{4})+(\frac{1}{2}\times \frac{22}{7}\times \frac{49}{4})+(\frac{1}{2}\times \frac{22}{7}\times \frac{21}{4}\times \frac{49}{4})c{m}^2$

$=(\frac{385}{16}+\frac{77}{4}\times \frac{1617}{16})c{m}^2$

$=\left(\frac{2310}{16}\right)c{m}^2$

$=144.375c{m}^2$