Question

Please help me with this

Answer 1

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$\sqrt{3}$ x 60
=30 x  5$\sqrt{3}$
= 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