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.