A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12 m.
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.

Solution:

Side of the equilateral triangle = 12 m

Area of the equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$

$=\frac{\sqrt{3}}{4} \times 12 \times 12$

$=62.28 \mathrm{~m}^{2}$

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°

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

$=\frac{60}{360} \times \frac{22}{7} \times(7)^{2}$

$=25.67 \mathrm{~m}^{2}$

Area of the field the horse cannot graze = Area of the equilateral triangle Area of the field the horse can graze

$=62.28-25.67=36.61 \mathrm{~m}^{2}$