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. Write the answer correct to 2 places of decimal.

Answer 1

Side of the equilateral triangle = 12 m
Area of the equilateral triangle =$\frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2$
$$\begin{gathered} =\frac{\sqrt{3}}{4}\times 12\times 12 \\ =62.28{\mathrm{m}}^2 \end{gathered}$$
Length of the rope = 7 m
Area of the field the horse can graze is the area of the sector of radius 7 m .Also, the angle subtended at the centre is 60$°$

=$\frac{\theta }{360}\times \mathrm{\pi }{r}^{\mathit{2}}$

$$\begin{gathered} =\frac{60}{360}\times \frac{22}{7}\times (7{)}^2 \\ =25.67{\mathrm{m}}^2 \end{gathered}$$

Area of the field the horse cannot graze = Area of the equilateral triangle $-$ Area of the field the horse can graze
$=62.28-25.67=36.61{\mathrm{m}}^2$