Another approach is to use Heron's area formula for a triangle gien the lengths of its three sides.

s = (a+b+c)/2 A=sqrt(s(s-a)(s-b)(s-c))

The two areas for 3,4,5 and 5,12,13 triangles works out to 6 and 30, so the sum is 36. I'm glad that answer matches yours, Bella!