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 . . .