The area of a right triangle


I right triangle i a triangle where the angle between two of the sides is $90°$. If you want to calculate the area of that triangle you need to know those two sides.

A right triangle with the sides a and b

The area is calculated with

$Area = \frac{a \cdot b}{2}$

Multiply the base and the hight with each other and divide with two.

It is easy to understand why this works if we know how to find the area of a rectangle. To calculate that you just multiply the base with the height. Let us study the triangle above inside a rectangle.

A rectangle with a right triangle drawn inside

You can see that the right triangle is exactly half of the rectangle above. That is way we divide the area of a rectangle in two to get the area of a right triangle.

Example 1

Find the area of the triangle.

The base is $3,4 \, cm$ and the height is $3.1 \, cm$. The area will be given by

$Area = \frac{3.4 \cdot 3.1}{2} = 5.27 \, cm^2$

Example 2

Find the area of the right triangle below.

We need to find the height of the triangle. Let us use the pythagorean theorem and call the height $h$.

$8.2^2=5.0^2+h^2$

Subtract with $5.0^2$

$8.2^2-5.0^2=h^2$

Calculate the left hand side.

$42.24=h^2$

Take the square root

$\sqrt{42.24}=h$

$h≈6.5\,m$

Now we know the height and we can calculate the area:

$Area = \frac{5.0 \cdot 6.5}{2} = 16.25 \, m^2$

Continue reading about pythagoras