# Area of isosceles triangle formula explained

Learn and know the formula used for finding area of isosceles triangle. We all know the formula for area of triangle $\frac { 1 }{ 2 }$bh where “b” means breadth and “h” means height. This formula can be used only when both height and breath are given.

When the sides are given then how to find area. There is one formula i.e. herons formula which can be used for finding area. But when comes to isosceles triangle, the same herons formula we can use but we have a special formula also for finding area. At first, we will discuss what is the meaning of the isosceles triangle and after that we will learn the formula for finding the area of it.

## What is mean by isosceles triangle in geometry?

I hope you know what is a triangle? In a triangle, if two (2) sides are of equal length then we call the triangle as an isosceles triangle. This is one of the types of triangles which come in classification of triangles based on sides in geometry chapter.

Note:

The angles which are opposite to equal sides are always equal and vice versa.

### The Formula for calculating the area of isosceles triangle as follows:

We know that in isosceles triangle any two sides are equal out of the three sides. Let us consider the length of the two sides which are equal be “p” units and the third side be “q” units. Then the formula for the area of isosceles triangle is given by $\frac { q }{ 4 }$ $\sqrt { 4{ p }^{ 2 }-{ q }^{ 2 } }$.

Examples:

What is the area of isosceles triangle if the equal sides are of 5 cm length and the third side is of 6 cm?

Solution:

We know that the formula for finding area of isosceles triangle is $\frac { q }{ 4 }$ $\sqrt { 4{ p }^{ 2 }-{ q }^{ 2 } }$, in this p is 5 cm and q is 6cm.

= $\frac { q }{ 4 }$ $\sqrt { 4{ p }^{ 2 }-{ q }^{ 2 } }$.

= $\frac { 6 }{ 4 }$ $\sqrt { 4 .{ 5 }^{ 2 }-{ 6 }^{ 2 } }$

= $\frac { 3 }{ 2 }$ $\sqrt { 100-36 }$

= $\frac { 3 }{ 2 }$ $\sqrt { 64 }$

= $\frac { 3 }{ 2 }$ x 8

= $\frac { 24 }{ 2 }$

= 12 sq.cm

So from now if there is a problem on area of the isosceles triangle, use the above given formula and find the answer.