Question

Find the area of the triangular field of sides 55 𝑚, 60 𝑚, and 65 𝑚. Find the cost of laying the grass in the triangular field at the rate of ₹8 per $m^2$.

Answer 1

Given,
a = 55m
b = 60m
c = 65m
Now,
S = (a + b + c ) /2 = (55 + 60 + 65)m/2 = 180m/2 = 90m.
Area =$\sqrt{s(s-a)(s-b)(s-c)}$
=$\sqrt{90(90-55)(90-60)(90-65)}$
=$\sqrt{90\times 35\times 30\times 25}$
= 150$\sqrt{105}{m}^2(\sqrt{105}=$ 10.2469508 ~ 10.25)
= $150\times 10.25$
= $1537.5m^2$
Now, cost of laying the grass in the triangular field is Rs.8 per $m^2$
So, total cost = Rs 1537.5×8 = Rs 12300