Question

Find the area of given figure, if the diameter BC is 14 cm and AD = 16 cm.

• A. $56c{m}^2$
• B. $77c{m}^2$
• C. $112c{m}^2$
• D. $189c{m}^2$

Answer 1

The correct option is D $189c{m}^2$

Given
BC = diameter = 14 cm
Hence
BD = DC = Radius = $\frac{diameter}{2}$ = $\frac{14}{2}$ = 7 cm

Area of given figure
= Area of $△$ABC + Area of semicircle

Area of $△$ABC
= $\frac{1}{2}\times base\times height$
$=\frac{1}{2}\times BC\times AD$
$=\frac{1}{2}\times 14\times 16=7\times 16=112c{m}^2$

Area of semicircle
$=\frac{1}{2}\times \pi r^2=\frac{1}{2}\times \frac{22}{7}\times D{C}^2=\frac{1}{2}\times \frac{22}{7}\times 7^2=\frac{1}{2}\times \frac{22}{7}\times 49=\frac{22\times 49}{7\times 2}=11\times 7=77c{m}^2$

Therefore, area of the given figure
= 112 + 77
= 189 $c{m}^2$