Area of an Equilateral Triangle
An equilateral triangle has three equal sides and angles. As in any type of triangle, its area is equal to half of the product of its base and height. So if the altitude of an equilateral triangle is:
The area of an Equilateral Triangle it will be defined by the following formula:
How do you find the area of an equilateral triangle?
The area of an equilateral triangle is obtained as the base product (side a) by the height (h) divided by two (Note: why is the area of a triangle a half of the base product by height?).
Let’s see what the height of the equilateral triangle.
Applying the Pythagorean theorem:
Another procedure to calculate its altitude would be from trigonometric ratios.
We obtain that the height (h) of equilateral triangle is:
Now, applying that area is a half of the product of base (a) by height (h):
And we arrive at the formula of the area of equilateral triangle is:
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.
Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.
Find the area of an equilateral triangle in which its three equal sides have the length a=5 cm.
What is its area?
Applying the above formula:
The area is 10.83 cm2.
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).
AUTHOR: Bernat Requena Serra