# Area of a Right Triangle

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*):

## Exercise

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:

And we have that the area is **6 cm ^{2}**.

## Finding the Area of a Right Triangle with the Geometric Mean 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:

So, we have the following formula:

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).