Right triangle and "b" are the legs of the triangle. If the incircle is tangent to the hypotenuse AB at point P, then denoting the semi-perimeter as "s", we have and , and the area is given by This formula only applies to right triangles. If an altitude is drawn from the vertex with the right angle to the hypotenuse then the triangle is divided into two smaller triangles which are both similar to the original and therefore similar to each other. From this: In equations, where "a", "b", "c", "d", "e", "f" are as shown in the diagram. Thus Moreover, the
Pappus's area theorem rather than only for right angled ones and secondly it uses parallelograms rather than squares. For squares on two sides of an arbitrary triangle it yields a parallelogram of equal area over the third side and if the two sides are the legs of a right angle the parallelogram over the third side will be square as well. For a right-angled triangle, two parallelograms attached to the legs of the right angle yield a rectangle of equal area on the third side and again if the two parallelograms are squares then the rectangle on the third side will be a