# Problem 390: Triangles with non rational sides and integral area

![graphic](img390.gif)

Consider the triangle with sides √5, √65 and √68. It can be shown that
this triangle has area 9. S(n) is the sum of the areas of all triangles
with sides √(1+b2), √(1+c2) and √(b2+c2) (for positive integers b and c
) that have an integral area not exceeding n. The example triangle has
b=2 and c=8. S(106)=18018206. Find S(1010).