A regular octagon rests on one of the flat sides and has a total height of 10 ft. What is the measure of one of the octagon’s sides ?

Question

I have to use a method like this : 360/7 = 51.42

51.42 = top of one angle

180 - 51.42 = 128.58

128.58/2 = 64.29

64.29 = side angle

Area = 1/2*Base*Height

tan (64.29) = h (7/2)

3.5 * tan (64.29)

h = 7.26, A = 1/2 (7) (7.26)

A = 25.41

25.41 * 7 = 177.87

Answer 1

Answer 2

Hello,

it looks like you are using an example with a seven-sided polygon. An octagon has 8 sides, so it is constructed from 8 congruent triangles, not 7. I am trying to use your steps, because you claimed you have to follow them.

360/8 = 45

45° = the top angle of an aforementioned triangle.

180 - 45 = 135

135/2 = 67.5

67.5° =one of the side angles in the triangle

(Area = 1/2*Base*Height -- this step is not relevant)

tan (67.5°) = h/ a (h=5ft,because it is half of the total height; a is half of the side of the octagon on question)

a * tan (67.5) = 5

a= 5/(tan(67.5))

a = 2.07 ft

The side of the octagon is 2*2.07 ft = 4.14 ft