Area of a regular polygon = 1/2 x apothem x perimeter
We know that each side is 10, because if you draw a segment from the center to a vertex it creates a 30-60-90 triangle (those are the angles). This type of triangle has a ratio for its sides where the longer side is radical three times as long as the shorter leg. This shorter leg happens to be half of a side of the polygon. Knowing that the polygon has 6 sides, we can multiply 10 by 6 to get the perimeter.
Area of polygon = 1/2 x apothem x perimeter = 1/2 x 5[tex] \sqrt{3} [/tex] x 60
=30 x 5[tex] \sqrt{3} [/tex]
= 30 x 5 x 1.73205080757
= 150 x 1.73205080757
= 259.807621135
To the nearest tenth of a cm, the area of the polygon is 260 cm squared
