What Is the Formula for the Area of a Triangle?

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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.

Formula

Area of a Triangle

A = base height 2

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 ÷ 3, or 60.

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

Rule

All sides are of equal length in an equilateral triangle.

All angles are 60.

A = base height 2

Example 1

Example of area of equilateral triangle with length 5 and 6

Example of area of equilateral triangle with length 5 and 6

The area of this equilateral triangle is

A = 6cm 5cm 2 = 15cm2

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.

Rule

The length of two sides are equal in an isosceles triangle.

Two angles are equal.

A = base height 2

Example 2

Example of area isosceles triangle with length 3 and 5

Example of area isosceles triangle with length 3 and 5

The area of this triangle is

A = 3cm 5cm 2 = 7.5cm2

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!

Rule

One angle is 90 in a right triangle.

A = base height 2

Example 3

Example of area of right triangle with length 3, 4 and 5

Example of area of right triangle with length 3, 4 and 5

The area of this triangle is

A = 3cm 4cm 2 = 6cm2

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.

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