Area of an Equilateral Triangle

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Drawing of the 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:

Formula for the height of the equilateral triangle

The area of an Equilateral Triangle it will be defined by the following formula:

Formula of the area of an equilateral triangle

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.

Drawing of the equilateral triangle for the calculation of its height

This can be calculated from Pythagorean theorem. The sides a, a/2 and h form a right triangle. The sides a/2 and h are the legs and a the hypotenuse.

Applying the Pythagorean theorem:

Calculation of the height of the equilateral triangle.

Another procedure to calculate its altitude would be from trigonometric ratios.

With respect to the 60º angle, the ratio between the height h and the hypotenuse of triangle a is equal to sine of 60º. Therefore:

Calculation of the height of the equilateral triangle for trigonometric ratios.

We obtain that the height (h) of equilateral triangle is:

Formula for the height of the equilateral triangle.

Now, applying that area is a half of the product of base (a) by height (h):

Calculation of the area of an equilateral triangle.

And we arrive at the formula of the area of equilateral triangle is:

Formula of the area of an equilateral triangle

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.

Exercise

Example 1 of equilateral triangle for calculating your area.

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:

Example 1 of the area of an equilateral triangle.

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).

Table of triangle area formulas for the reasons we know

AUTHOR: Bernat Requena Serra

YEAR: 2018


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