Question

A horse is placed for grazing inside a rectangular field 70 m by 52 m and is tethered to one corner by a rope 21 m long. Find the area ungrazed by the horse.

Answer 1

The horse can graze in the sector EAF.
Length of the rope =21 m
$\therefore$ Radius of the sector EAF =21 m
$\angle A={90}^{\circ }$ [ Angle of rectangular field ]
$\therefore$ Area of the sector EAF $=\frac{\text{/}{90}^1}{\text{/}{360}_4}\times \pi r^2$
$=\frac{1}{4}\times \frac{22}{7}\times (21{)}^2{m}^2$
$=\frac{1}{4}\times \frac{22}{\text{/}7}\times 21\times \text{/}{21}^3{m}^2$
$=\frac{1386}{4}{m}^2=346.5m^2$
Area ungrazed =3640 - 346.5
$=3293.5m^2$