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Question
A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12 m. If the length of the rope is 7 m, find the area of the field which the horse cannot graze. Write the answer correct to 2 places of decimal.
Solution
Side of the equilateral triangle = 12 m
Area of the equilateral triangle `= sqrt(3)/4xx("Side")^2`
`=sqrt(3)/4xx12xx12`
Length of the rope = 7 m
Area of the field the horse can graze is the area of the sector of radius 7 m .Also, the angle subtended at the centre is 60°
`=theta/360xxpi"r"^2`
`=60/360xx22/7xx(7)^2`
= 25.67 m2
Area of the field the horse cannot graze = Area of the equilateral triangle -- Area of the field the horse can graze
= 62.28 - 25.67 = 36.61 m2
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