Q33 of 40 Page 1

Sides of a right triangular field are 25m, 24m and 7m. At the three corners of the field, a cow, a buffalo and a horse are tied separately with ropes of 3.5 m each to graze in the field. Find the area of the field that cannot be grazed by these animals.

64.75 m2



Given – sides of triangle : 24m, 25m, 7m , radii of three circles : 3.5 m


Answer –


We know that, area of triangle is



In above figure, base b = 7 and height h = 24


Therefore, area of ∆ABC is



∴ A = 84 m2 ………(1)


Now, sum of three angles of a triangle is 180⁰.


If we join portions of three circles with radii 3.5 we get sector of angle 180⁰ that is semicircle.


Area of this semicircle of radius 3.5 m is




∴ A’ = 19.25 m2


Therefore, area of field that cannot be grazed by animals


= area of triangular field – sum of areas of 3 sectors


= 84 – 19.25


= 64.75 m2


Therefore, area of field that cannot be grazed by animals is 64.75 m2.


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