Question

A horse is placed for grazing inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope 21 m long. On how much area can it graze? How much area is left ungrazed?

Answer 1

Radius of the quadrant of the circle = 21 m
The shaded portion shows the part of the field the horse can graze.

Area of the grazed field = Area of the quadrant OPQ
$=\frac{1}{4}\mathrm{of}\mathrm{the}\mathrm{circle}\mathrm{having}\mathrm{radius}\mathrm{OP}$
$$\begin{gathered} =\frac{1}{4}{\mathrm{\pi r}}^2 \\ =\frac{1}{4}\times \frac{22}{7}\times 21\times 21 \\ =346.5{\mathrm{m}}^2 \end{gathered}$$

Total area of the field = $70\times 52=3640{\mathrm{m}}^2$

Area left ungrazed = Area of the field $-$ Area of the grazed field
= $3640-346.5=3293.5{\mathrm{m}}^2$