information:filtering
Area

As with any triangle, the area is equal to one half the base multiplied by the corresponding height. In a right triangle, if one leg is taken as the base then the other is height, so the area of a right triangle is one half the product of the two legs. As a formula the area T {\displaystyle T} is

where a {\displaystyle a} and b {\displaystyle b} are the legs of the triangle.

If the incircle is tangent to the hypotenuse A B {\displaystyle AB} at point P, {\displaystyle P,} then letting the semi-perimeter be s = 1 2 (a + b + c), {\displaystyle s={\tfrac {1}{2}}(a+b+c),} we have | P A | = s − a {\displaystyle |PA|=s-a} and | P B | = s − b, {\displaystyle |PB|=s-b,} and the area is given by

This formula only applies to right triangles.