This requires a scientific calculator with the "cos" key.

8 sides - 2 = 6
6 * 180 = 1080
1080 / 8 sides = 135 degrees
135 degrees / 2 = 67.5 degrees
67.5 degrees(cos) * 12" = 4.592201"

5 sides - 2 = 3
3 * 180 = 540
540 / 5 sides = 15 degrees
15 degrees / 2 = 7.5 degrees
7.5 degrees(cos) * 12" = 11.89733834"

12 sdies - 2 = 10
10 * 180 = 1800
1800 / 12 sides = 150 degrees
150 degrees / 2 = 75 degrees
75 degrees(cos) * 12" = 3.105828541"