## AREA OF A TRIANGLE

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(x1, y1), B(x2, y2) and C(x3, y3).

Draw

We know that,