Question

proof area of triangle is √s(s-a)(s-b)(s-c)

​

Answer 1

According to Heron, we can find the area of any given triangle, whether it is a scalene, isosceles or equilateral, by using the formula, provided the sides of the triangle.

Suppose, a triangle ABC, whose sides are a, b and c, respectively. Thus, the area of a triangle can be given by;

Area=root s(s−a)(s−b)(s−c)

Where “s” is semi-perimeter = (a+b+c) / 2

And a, b, c are the three sides of the triangle.

How to Find the Area Using Heron’s Formula?

To find the area of a triangle using Heron’s formula, we have to follow two steps:

The first step is to find the value of semi-perimeter of the given triangle.  

S = (a+b+c)/2

The second step is to use Heron’s formula to find the area of a triangle.

Let us understand that with the help of an example.

Example: A triangle PQR has sides 4 cm, 13 cm and 15 cm. Find the area of the triangle.

Semiperimeter of triangle PQR, s = (4+13+15)/2 = 32/2 = 16

By heron’s formula, we know;

A = √[s(s-a)(s-b)(s-c)]

Hence, A = √[16(16-4)(16-13)(16-15)] = √(16 x 12 x 3 x 1) = √576 = 24 sq.cm

This formula is applicable to all types of triangles. Now let us derive the area formula given by Heron.