Question

What is Heron’s formula?

Answer 1

Hint: We are asked to write Heron’s formula for which you need to be aware about various formulae related to the triangle. The general formula while writing the area of the triangle mostly assumes the triangle to be a right angled triangle but since we are not always sure whether the triangle would be right angled or not we need a formula which uses only the length of each side to calculate its area and Heron’s formula basically does that.

Complete step by step solution:
In the given question we are asked about what is Heron’s formula which is basically meant to find the area of the triangle when the sides are also given. When we are given the three sides of triangles then we can apply this formula to find the area.
Heron formula involves the semi-perimeter which means that we need to sum the length of all sides of the triangle and then half the value attained which is called the semi-perimeter and the full value of the sum of lengths attained is called the perimeter.

Semi-perimeter is given by $\dfrac{{{s}_{1}},{{s}_{2}},{{s}_{3}}}{2}$ where s denotes the semi perimeter and ${{s}_{1}},{{s}_{2}},{{s}_{3}}$ are the three different sides of the triangle.
Using these we need to write the heron’s formula as
$A=\sqrt{s(s-{{s}_{1}})(s-{{s}_{2}})(s-{{s}_{3}})}$
Hence, the Heron’s formula has been explained.

Note: While calculating the area using Heron's formula, one generally forgets to divide the perimeter by 2, so whenever you calculate the perimeter make sure that you find the semi perimeter and put that as the value of $s$. Also, be very careful while calculating the square root because there are high chances of calculation mistakes there.