Question

Three horses are tied each with 7 m long rope at three corners of a triangular field having sides 20 m, 34 m and 42 m. Find the area of the plot which can be grazed by the horses.

Answer 1

Let ∠A = θ₁, ∠B = θ₂ and ∠C = θ₃

We have,

r = 7 m, a = 34 m, b = 42 m and c = 20 m   ...(Where, BC = a, AC = b and AB = c)

Now, area which can be grazed by the horses = sum of the areas of three sectors with central angles θ₁, θ₂ and θ₃ each with radius (r) = 7 m

= `(πr^2θ)/360^circ + (πr^2θ)/360^circ + (πr^2θ)/360^circ`

= `(πr^2)/360^circ (θ_1 + θ_2 + θ_3)`

= `(πr^2)/360^circ xx 180^circ`   ...[∵ θ₁ + θ₂ + θ₃ = 180° angle sum property of a triangle]

= `(≠r^2)/2`

= `22/7 xx 1/2 xx (7)^2`

= `22/7 xx 1/2 xx 7 xx 7`

= 77 m²

Hence, the area grazed by the horses is 77 m².