The regular exagon (polygon in the figure) is equilateral and equiangular.
You can divide all the sides in triangles...
That thing that measures 5√3 cm is the apotheme.
The apotheme divides the equilateral triangles in half so the halves are 30° - 60° - 90° triangles and then we know that the apotheme is x√3 so...
x√3 = 5√3 -> divide both for √3
x = 5
This is the base of the halves, thus the base of the entire triangle is 10. We find the perimeter of the exagon -> 10*6 = 60 cm
We can find the area = 1/2 * perimeter * apotheme
1/2*60*5√3 = 150√3 cm²
