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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?
Solution
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
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