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

`=1/4` of the circle having radius OP

`=1/4pi"r"^2`

`=1/4xxpi"r"^2`

`= 1/4 xx 22/7xx21xx21`

= 346.5 m² 

Total area of the field = 70 × 52 = 3640 m² 

Area left ungrazed = Area of the field -- Area of the grazed field

= 3640 - 346.5 = 3293.5 m²