Question

A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12 m. If the length of the rope is 7 m, find the area of the field which the horse cannot graze. Take $\sqrt{3}$ = 1.732. Write the answer correct to 2 places of decimal.

Answer 1

$Area\left(ABC\right)=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}\times 12\times 12=36\sqrt{3}{m}^2$
Horse can graze only in sector BDE.

$area\left(BDE\right)=\frac{\theta }{360}\times \pi r^2=\frac{60}{360}\times \frac{22}{7}\times 7\times 7=\frac{1}{6}\times 22\times 7=\frac{1}{3}\times 11\times 7=\frac{77}{3}{m}^2$

Area remains ungrazed $=36\sqrt{3}-\frac{77}{3}=62.35-25.67=36.68m^2$