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 `= sqrt(3)/4xx("Side")^2` 

`=sqrt(3)/4xx12xx12`

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°

`=theta/360xxpi"r"^2`

`=60/360xx22/7xx(7)^2`

= 25.67 m² 

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 m²