The coordinates of seven vertices of a 7-gon are generated by the following rule $$f(x) = (x - 7)^2 + 3$$ for $$x \in \{4, 5, 6, 7, 8, 9, 10\}$$. Find the area of the polygon.

The vertices are $$(4, 12)$$, $$(5, 7)$$, $$(6, 4)$$, $$(7, 3)$$, $$(8, 4)$$, $$(9, 7)$$, $$(10, 12)$$, and the closing side is the line $$y = 12$$. Splitting into vertical strips of width 1, the areas below $$y = 12$$ are $$2.5$$, $$6.5$$, $$8.5$$, $$8.5$$, $$6.5$$ and $$2.5$$. The total area is 35 sq. units.