Isosceles Triangle Area Calculator

Created by Rijk de Wet
Reviewed by Aleksandra Zając, MD
Last updated: Jun 01, 2022

Welcome 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:

  1. Enter the dimensions that you know from among the legs, base, and height.
  2. Find the area of the isosceles triangle you described.
  3. 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 aa. The remaining side is called the base and has length bb. An isosceles triangle is usually drawn so that the base lies horizontally at the bottom:

An isosceles triangle with its sides, angles and heights marked.
An isosceles triangle. Note that the legs marked aa are the same length, and the corners marked α\alpha are the same angle.

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:

A=12×b×hA = \frac{1}{2} \times b \times h

where

  • AA is the area of the isosceles triangle;
  • bb is the base side's length; and
  • hh 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 hh with the Pythagorean theorem:

h=a2(b2)2h = \sqrt{a^2 - \left(\frac{b}{2}\right)^2}

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.

If you found this isosceles triangle area calculator too obtuse for your needs, you might try:

FAQ

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 cm2. The two legs are 13 cm and the base 24 cm (although you can use any unit you want).

  1. Calculate the height of this triangle with the Pythagorean theorem:
    h = √[ a2 − (b/2)2 ]
    = √[ (13)2 − (24/2)2 ]
    = 5 cm
  2. Calculate the area of this triangle with the standard formula:
    A = ½ × h × b
    = ½ × 24 × 5
    = 60 cm2

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.

Rijk de Wet
isosceles triangle with sides, angles and heights marked.
Leg (a)
in
Base (b)
in
Height (h)
in
Area
in²
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