Question

The sides of a triangular field are 325 m, 300 m and 125 m. Its area is

Answer 1

We've been given the dimensions of a triangular field, and we are asked to find the area.

Let the sides be a, b & c.

a = 325m

b = 300m

c = m.

We can use Heron's formula to find out the area of this triangle.

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{s\Big(s-a\Big)\Big(s-b\Big)\Big(s-c\Big)}$

Where a, b and c are the sides and s is the semi perimeter.

Semi-perimeter:

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

$\sf \Longrightarrow s = \dfrac{325 + 300 + 125}{2}$

$\sf \Longrightarrow s = \dfrac{750}{2}$

$\sf \Longrightarrow s = 375$

Now, let's find the area of the triangle using Heron's formula.

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{s\Big(s-a\Big)\Big(s-b\Big)\Big(s-c\Big)}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{375\Big(375-325\Big)\Big(375-300\Big)\Big(375-125\Big)}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{375\Big(50\Big)\Big(75\Big)\Big(250\Big)}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{ \Big(3 \times 5 \times 5 \times 5\Big) \Big(2 \times 5 \times 5 \Big)\Big( 3 \times 5 \times 5 \Big)\Big(2 \times 5 \times 5 \times 5\Big)}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{3 \times 5 \times 5 \times 5 \times 2 \times 5 \times 5 \times 3 \times 5 \times 5 \times 2 \times 5 \times 5 \times 5}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{3 \times 3 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = \sqrt{3^2 \times 2^2 \times 5^2 \times 5^2 \times 5^2 \times 5^2 \times 5^2}$

$\sf \Longrightarrow Area \ of \ a \ \triangle = 3 \times 2 \times 5 \times 5 \times 5 \times 5 \times 5$

$\sf \Longrightarrow Area \ of \ a \ \triangle = 6 \times 25 \times 25 \times 5$

$\sf \Longrightarrow Area \ of \ a \ \triangle = 30 \times 625$

$\sf \Longrightarrow \underline{\underline{\bold{Area \ of \ a \ \triangle = 18750 \ m^2}}}$

Answer: 18750 m²