Question

If the semi circular lawns are made on all sides of an equilateral triangular field of side 7 m. Find total area of the field with lawns. $(\sqrt{3}=1.732)$

• A. $78.967m^2$
• B. $70.367m^2$
• C. $75.667m^2$
• D. $87.567m^2$

Answer 1

The correct option is A $78.967m^2$

Let $ABC$ be the equilateral triangle whose sides $=7cm$

Then in the given cirecle

$d=7cm$

and $r=7/2cm$

Now,

Required area $=\frac{\sqrt{3}}{4}\times {\left(side\right)}^2+\frac{3}{2}\pi r^2$

$=\frac{\sqrt{3}}{4}\times {\left(7\right)}^2+\frac{3}{2}\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$

$=\frac{49\sqrt{3}}{4}+\frac{66\times 7}{8}\left[divide66\&8by2weget33\&4respectively\right]$

$=\frac{49\sqrt{3}}{4}+\frac{231}{4}$

$=\frac{49\times 1.732+231}{4}$

$=78.96c{m}^2$

Hence, the option $\left(A\right)$ is correct.