Consider a triangle as shown below:

**The most common formula to find the area of the triangle is . **

In any triangle, the area of the triangle is given by

Where, *b* is the length of the base of the triangle and *h* is the length of the altitude drawn to an extension from the base.

__Area of a triangle when three sides of a triangle are given (SSS):__

A Greek philosopher and mathematician, **Heron **formulates a formula to find the area of a triangle, when the lengths of the three sides are given. This formula is known as ** Heron’s formula, **which is written as follows:

Where *a, b,* and *c* are the lengths of the three sides of a triangle, and s is the semi perimeter.

__Question 1__

Find the area of the triangle when the lengths of base and height are12 meter and 16 meter.

__Solution 1__

Known the lengths of base and height, use the formula

Substitute the value as follows:

Therefore, the area of a triangle is 96 square meter.

__Question 2__

What is the area of a triangle when three sides are 6 cm, 4 cm and 20 cm.

__Solution 2__

Since three sides of a triangle are known then, use the formula

Find the value of s as follows:

Substitute the value as follows:

Therefore, the area of the triangle is 86. 17square centimeter.

__Area of triangle when vertices are given:__

Consider a triangle ABC, whose vertices are A(x_{1}, y_{1}), B(x_{2}, y_{2}) and C(x_{3}, y_{3}).

Draw

We know that,