# Area of scalene triangle formula explained

Learn and know the formula for finding the value of area of scalene triangle in mensuration. For any kind of triangle, we need to learn two important formulas. The first one is formula for perimeter and the second one is formula for area.

Now we are going to learn the formula for area of scalene triangle. But first we should know what is the meaning of scalene triangle? So first we will discuss scalene triangle definition and then we will know the formula for area.

## What is scalene triangle?

A triangle is called as a scalene triangle if the three sides of the triangle are different in dimensions. Or we can also give the definition of scalene triangle as “in a triangle, if no two sides are equal then it is called as a scalene triangle”.

### Formula for area of scalene triangle as follows:

We know that for a scalene triangle, all the three sides will be different. Let the three sides of scalene triangle be “a”, “b” and “c” units. Then the formula for area of scalene triangle is given as $\sqrt { s\times \left( s-a \right) \times \left( s-b \right) \times \left( s-c \right) }$ square units. Here S is semi-perimeter, which means half of the perimeter and is given as $\frac { \left( a+b+c \right) }{ 2 }$. This formula can be used for any kind of triangle not only for scalene triangle. If the sides of the triangle are known then we find the area for any triangle.

Example:

The sides of the triangle are given as 4cm; 6cm and 8cm. find the area.

Solutions:

First find semi perimeter i.e. S = $\frac { \left( 4+6+8 \right) }{ 2 }$ = 9

sa = 9 – 4 = 5

sb = 9 – 6 = 3

sc = 9 – 8 = 1

s × (sa) × (sb) × (sc) = 9 × 5 × 3 × 1 = 135.

Therefore area =$\sqrt { 135 }$ = 11.62 (approximately)