Last updated: Jul 15, 2024

Isosceles Triangle Area Calculator

Q: 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

Q: 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.

Created by Rijk de Wet

Rijk de Wet

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Holds a Master's degree in Data Science / Industrial Engineering, obtained at Stellenbosch University, South Africa. His research investigates using swarm intelligence to solve data clustering and other optimization problems. Will never refuse an offer to play some board games. See full profile

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Reviewed by Aleksandra Zając, MD

Aleksandra Zając

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A young Medical Doctor certified International Board of Lifestyle Medicine Diplomate. In one of the big Warsaw clinics, she's responsible for prophylaxis and medical education. Professionally interested in nutrition, exercise, and mental health. She wants never to stop learning and currently studies postgraduate psychodietetics. She likes to bake and play with her pets – one dog and four fancy mice. See full profile

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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 calculators FAQs

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:

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:

An isosceles triangle with its sides, angles and heights marked. — An isosceles triangle. Note that the legs marked $a$ are the same length, and the corners marked $\alpha$ 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 = \frac{1}{2} \times b \times h

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:

h = \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.

FAQs

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).

Calculate the height of this triangle with the Pythagorean theorem:
h = √[ a² − (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 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.