# Isosceles Triangle Area Calculator

Table of contents

How do I use the isosceles triangle area calculator?What is an isosceles triangle?How do I find the area of an isosceles triangle?Related calculatorsFAQsWelcome to the **isosceles triangle area calculator**, where we will teach you all there is to know about the area of an isosceles triangle! We'll specifically show you how to calculate the area of an isosceles triangle to find it yourself by hand.

## How do I use the isosceles triangle area calculator?

Using the isosceles triangle area calculator is easy:

**Enter**the dimensions that you know from among the**legs, base, and height**.**Find**the area of the isosceles triangle you described.- The isosceles triangle area calculator can also work
**backward**— enter the area and some of the side lengths, and the calculator will work out the other sides.

## What is an isosceles triangle?

An isosceles triangle is a triangle with two equal sides. The two equal sides are called the **legs** and have length $a$. The remaining side is called the **base** and has length $b$. An isosceles triangle is usually drawn so that the base lies horizontally at the bottom:

## How do I find the area of an isosceles triangle?

Our isosceles triangle area calculator is great, but you won't have it in an exam. So, let's learn how to calculate the area of an isosceles triangle. An isosceles triangle follows the same **area formula** as any other triangle:

where

- $A$ is the area of the isosceles triangle;
- $b$ is the base side's length; and
- $h$ is the triangle's height.

The trick for **how to find the area of an isosceles triangle** is to calculate its height, because that is usually unknown. If you know the length of the isosceles triangle's legs, you can easily calculate $h$ with the Pythagorean theorem:

Knowing the height allows you to use the **standard triangle area equation** we showed above.

And there you have it! Now you know how to calculate the area of an isosceles triangle.

### How do I find the area of an isosceles triangle without the height?

You can use other methods of finding the isosceles triangle's height:

- If you have the sides' lengths
`a`

and`b`

, you can use the Pythagorean theorem to calculate the height`h`

:

`h = √[ a² − (b/2)² ]`

- If you have the base angle
`α`

and a side length`a`

or`b`

, you can use trigonometry to calculate the height:

`h = ½×a×tan(α) = b×sin(α)`

Once you have the height, you can work out the area with `A = ½ × b × h`

.

### What is the area of an isosceles triangle with sides 13, 13, and 24?

The area of this triangle is **60 cm ^{2}**. The two legs are 13 cm and the base 24 cm (although you can use any unit you want).

- Calculate the height of this triangle with the Pythagorean theorem:

h = √[ a^{2}− (b/2)^{2}]

= √[ (13)^{2}− (24/2)^{2}]

= 5 cm - Calculate the area of this triangle with the standard formula:

A = ½ × h × b

= ½ × 24 × 5

= 60 cm^{2}

### Are all equilateral triangles isosceles?

**It depends on the exact definition** you're using for isosceles triangles. Some say that an isosceles triangle has **exactly** two equal sides, which would disqualify an equilateral triangle from being considered isosceles. Others say that an isosceles triangle has **at least** two equal sides. An equilateral has three equal sides, so in this case, an equilateral triangle is isosceles too.