This regular octagon has a side length 15.0cm. Determine the distance from one vertex to the opposite vertex, measured through the centre of the octagon. Give your answer to to the nearest tenth of a centimeter.

Answer 1

Divide the octagon into 8 congruent isosceles triangles, each with base 15.

Since the vertex angle is 360/8 = 45°, each of the slant sides has length

7.5/sin22.5° = 19.6

The desired distance is twice the length of one of these sides, or 39.2

Answer 2

Where did you get 7.5 and 22...