Question

Find the area of the regular polygon below and round your answer to the nearest hundredth.

Answer 1

The central angle of each sector is 360°/8 = 45°, so the central angle between a vertex and the apothem is half that, 22.5°. The length of half a side will be
  s/2 = (2 ft)*tan(22.5°) ≈ 0.828427 ft
The area of each of the 8 sectors will be this multiplied by the apothem (2 ft), so is 1.6568 ft². The total area of the 8 sectors is then
  8*1.6568 ft² ≈ 13.25 ft²