Sides of a triangular field are 15 m, 16 m, and 17m. with the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7m each to graze in the field.
Find the area of the field which cannot be grazed by the three animals.

Question

Philoid · Accepted Answer

Sides of the triangle are 15 m, 16 m, and 17 m.

Now, perimeter of the triangle = (15+16+17) m = 48 m

∴ Semi-perimeter of the triangle = s = 48/2 = 24 m

By Heron’s formula, Area of the triangle =

(where a, b, c are the sides of triangle)

=

= 109.982 m²

Let B, C and H be the corners of the triangle on which buffalo, cow and horse are tied respectively with ropes of

7 m each.

So, the area grazed by each animal will be in the form of a sector.

∴ Radius of each sector = r = 7 m

Let x, y, z be the angles at corners B, C, H respectively.

∴ Area of sector with central angle x =

Area of sector with central angle y =

Area of sector with central angle z =

Area of field not grazed by the animals = Area of triangle – (area of the three sectors)

=

= 109.892 – 77 = 32.982 cm²

Sides of a triangular field are 15 m, 16 m, and 17m. with the three corners of the field a cow, a buffalo and a horse are tied separately with ropes of length 7m each to graze in the field.Find the area of the field which cannot be grazed by the three animals.