Question

The sides of a triangle are 122 m, 22 m and 120 m respectively. The area of the triangle is:Only by Heron's formula ​

Answer 1

A=122m

B=22m

C=120m

$s = \frac{a + b + c}{2}$

S=132m

$area = \sqrt{s(s - a)(s - b)(s - c)}$

Putting the values of a b and c

Area=1320cm^2

Answer 2

Given : The sides of a triangle are 122 m, 22 m and 120 m respectively.

To find : The area of the triangle. (using Heron's formula)

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the area of the given triangle)

First side of the triangle (a) = 122 m

Second side of the triangle (b) = 22 m

Third side of the triangle (c) = 120 m

Now, we have to call the semi-perimeter (s) of the given triangle.

So, the semi-perimeter (s) of the triangle :

= (a + b + c)/2

= (122 + 22 + 120)/2

= 132 m

According to the Heron's formula, the area of the triangle will be :

$= \sqrt{s \times (s - a) \times (s - b) \times (s - c)}$

[ s = semi-perimeter ; a,b and c = three sides of the triangle]

By, putting the available data in Heron's formula, we get :

= $\sqrt{132 \times (132 - 122) \times (132 - 22) \times (132 - 120)}$

$= \sqrt{132 \times 10 \times 110 \times 12}$

$= 1320 {m}^{2}$

(This will be considered as the final result.)

Hence, the area of the triangle is 1320m².