Area of a Triangle Using the Base and Height

The area of any triangle can be calculated by knowing one side and the height (or altitude), associated with that side. This side serves as the base.

In fact the most common way to calculate the area of a triangle is to take half of the base (b) times the height (h). That’s:

Practice Problem

The length of the base (b) of a triangle is 4 cm and its related altitude (h) is 2 cm. Find the area of the triangle.

Solution:

We just apply the general formula for calculating the area of a triangle: ½ · (b · h).

So, the area of the triangle is 4 cm².

How Do you Get the Formula of the Area of a Triangle?

Let’s see the figure above: a triangle can be inscribed in a rectangle of base b and height h. In other words, a parallelogram can be divided into two triangles. So, if the area of a rectangle is A = b · h, the area of a triangle is A = ½ · (b · h).

Indeed, the area of triangle ABC is the sum of the area of right triangle T1 and that of right triangle T2. These two right triangles are inside the rectangle, which is completed with the triangles T1 and T2, that are equal to the previous ones.

Thus, the area of a triangle ABC is half the area of a rectangle whose sides are b and h:

Table of Triangle Area Formulas

You can see the table of triangle area formulas . Depending on the type of triangle you may need one element ( equilateral triangle), two (base and height) or three (as long as they are not the three angles).