In a right triangle, the radius of the incircle equals r and the area equals A. If the triangle's hypotenuse has length h, the area A equals:

1. In a right triangle, semi-perimeter s = (a + b + h)/2 where a, b are the legs. 2. For a right triangle the tangent length from the right-angle vertex is r itself. 3. From this one can show s = h + r (textbook problem 5 of Ch 7). 4. Area A = r × s = r × (h + r). 5. So A = r(h + r). _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._