What Is the Formula for the Area of a Triangle?

When calculating the area of a triangle, you need two pieces of information: You need to know the length of the base, and the height of the triangle. But the height can’t be just any height. It must be the perpendicular height of the triangle. That means you must take the distance from the base to the opposite corner. This line and base must form a $90$° angle.

You will now learn about finding the area of different types of triangles. The formula remains the same.

Equilateral Triangles

Let’s start by taking a look at the area of an equilateral triangle. An equilateral triangle is a triangle where all sides are equal in length, and all angles are equal. Since the sum of the angles of a triangle is $180$°, each angle is equal to $180\text{°}÷3$, or $60\text{°}$.

When calculating the area of an equilateral triangle, you just need to know the length of the base and the height of the triangle.

Isosceles Triangles

Now we’ll work on the area of an isosceles triangle. An isosceles triangle is a triangle where two of the three sides are of equal length. It follows that two of the angles are equal as well. We often call the equal sides the legs, and the third side is often referred to as the base.

To calculate the area of an isosceles triangle, you just need to know its height, and the length of the base.

Right Triangle

A right triangle is a triangle where one angle is a right angle—equal to $90$°. None of the sides of a right triangle must be the same length. When calculating the area of a right triangle, you must know the lengths of the two shorter sides, because one of the shorter sides is the base, and the other shorter side is the height!

Finding the area of a triangle is often a simple procedure, especially because the formula is the same for all types of triangles. You may have also noticed that the area of a triangle is the same as taking exactly half the area of a rectangle.