Area of a Triangle Using the Base and Height

1 Star2 Stars3 Stars4 Stars5 Stars (No Ratings Yet)
Loading...

Drawing of the triangle with known 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:

Formula for the area of a triangle with known base and height

Download this calculator to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar         or   Triangle-total.exe      

Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.

Practice Problem

Example of a triangle with known base and height

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).

Calculation of the area of an example of a triangle with known base and height

So, the area of the triangle is 4 cm2.

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

Drawing of the triangle with known base and height for your demonstration

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:

Formula for the area of a triangle with known base and height

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).

Table of triangle area formulas for the reasons we know

AUTHOR: Bernat Requena Serra

YEAR: 2020


IF YOU LIKED IT, SHARE IT!

Leave a Reply

Your email address will not be published.