MathDB

Consider an equilateral triangular grid

G

with

20

points on a side, where each row consists of points spaced

1

unit apart. More specifically, there is a single point in the first row, two points in the second row, ..., and

20

points in the last row, for a total of

210

points. Let

S

be a closed non-self-intersecting polygon which has

210

vertices, using each point in

G

exactly once. Find the sum of all possible values of the area of

S

30