Question

A horse is tethered to one corner of a rectangular field of dimensions 70 m by 52 m by a rope 28 m long for grazing. How much area can the horse graze inside? How much area is left ungrazed?

Answer 1

Length of the rectangle, l $=70$ m
Breadth of the rectangle, b $=52$ m
Length of the rope $=28$ m
Shaded portion AEF indicates the area in which the horse can graze. Clearly, it is the area of a quadrant of a circle of radius, r $=28$ m
Area of the quadrant AEF $=\frac{1}{4}\times \pi r^2$ sq. units
$=\frac{1}{4}\times \frac{22}{7}\times 28\times 28=616m^2$
$\therefore$ Grazing Area = 616 m${}^2$
Area left ungrazed = Area of the rectangle ABCD - Area of the quadrant AEF
Area of the rectangle ABCD = $l\times b$ sq. units
$=70\times 52=3640m^2$
$\therefore$ Area left ungrazed $=3640-616=3024$ m${}^2$.