Geometry
posted by Brie .
Assume each side of the hexagon is worth 10 units. Calculate the apothem, using the fact that it is part of a special triangle to get the answer exactly. Then use the exact value of the apothem to calculate the area of the hexagon.

the apothem is the altitude of an equilateral triangle of side 10: 5√3
area = 1/2 apothem * perimeter = 1/2 * 5√3 * 10 = 25√3