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 cm².

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.

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).