Inscribed Circle into a triangle

A circle is inscribed in a right triangle and the point where the circle touches the hypothenuse divides the hypothenuse in two parts(m & n). What is the surface area of the triangle (expressed through m & n). I know to calculate the surface area when the circle divides the side in m & n but not in this case.

See the picture for info

a^2 +(a+m-n)^2=(m+n)^2
a^2 +a^2+(m-n)^2+2*a(m-n)=(m+n)^2
a^2+a(m-n)/2-2mn=0
a=(m-n)/4 + sqr((m/n)^2/16+2mn)
A= a*(a+m-n)/2