Area of a Right Triangle

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Right triangle drawing

The right triangle has a right angle (90°), so its height coincides with one of its sides (a) and its base with the other side (b).

The area of a right triangle is half the product of the two sides that form the right angle (legs a and b):

Formula for the area of a right triangle

Exercise

Example of a right triangle to calculate its area

Find the area of a right triangle given its two legs, which form the right angle: a = 3 cm and b = 4 cm.

Solution:

Apply the above formula:

Example of the area of a right triangle

And we have that the area is 6 cm2.

Finding the Area of a Right Triangle with the Geometric Mean Theorem

Drawing of the right triangle in the height theorem

The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.

If the altitude (h) is drawn to the hypotenuse (c) of a right triangle, each leg (a and b) of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg (n or m).

Then:

Altitude of a right triangle by the height theorem

So, we have the following formula:

Formula for the area of a right triangle by the height theorem

This is a useful method if the legs (a and b) are unknown.

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.

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


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