Hello, gollum!

I used some Olympic-level gymnastics . . .

Integers satisfying the equation:

are vertexes of a certain polygon. .What is its area?

We have a quadratic in

Quadratic Formula: .

. .

Since is an integer, the radicand must be a square.

. . . . . .

Hence, we have: .

The difference of two squares is 20.

. . The only such squares are: .

This gives us: .

. . . . . . and: .

We have four vertices:

. .

We have a parallelogram with base 4 and height 5 . . .