Recall: Area of a polygon is half the product of the apothem and the perimeter. Since the apothem is always perpendicular to a side of the polygon, we can use special right triangles and trig to help us solve for each value in the formula.
In special cases (hexagons, triangles, squares) the regular polygon has a built in special right triangle, so we don't need trig to solve for the area and we can solve for it exactly!
Some regular polygons don't have built in special triangles. In these cases we need to use trig to solve for the area!
