Question

Q4: 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 Rs 8 per m2.

Answer 1

$\sf \: s = \dfrac{a + b + c}{2}$

$\dashrightarrow\sf \: s = \dfrac{55 + 60 + 65}{2}$

$\dashrightarrow\sf \: s = \dfrac{180}{2}$

$\dashrightarrow\sf \: s = \cancel \dfrac{180}{2}$

$\dashrightarrow\sf \: s = 90$

Area:-

$\dashrightarrow \sf \: A = \sqrt{s(s - a)(s - b)(s - c)}$

$\dashrightarrow \sf \: A = \sqrt{90(90 - 55)(90 - 60)(90 - 65)}$

$\dashrightarrow \sf \: A = \sqrt{90 \times 35 \times 30 \times 25}$

$\dashrightarrow \sf \: A = \sqrt{2,362,500}$

$\dashrightarrow \sf \: A = \bf 1537.04m^2$

Cost:-

Cost of 1 m² = 8

Cost of 1537.04m² =₹ 8 × 1537.04

Cost of 1537.04m² =₹ 12,296.32

sorry for less steps, I am pretty lazy!~

Answer 2

Answer:

Sides of the triangle are a=55m,b=65m,c=65m

Area of triangle, by Heron's formula =s(s−a)(s−b)(s−c)

where, 

s=2a+b+c

s=250+65+65

s=90

Area of triangle = 90(40)(25)(25)

Area of triangle = m2

Cost of laying grass = Area ×8

Cost of laying grass =1537.04

Cost of laying grass = Rs 12.296.32