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