Geometry

We can  divide the octagon into 8 congruent triangles

AB = the base of each = 1

Height = h   of each triangle  can be found as

(1/2) / sin (22.5°)  =  h / sin (67.5 °)

(1/2) / sin (22.5°) = h / cos (22.5°)

h = (1/2) cos (22.5°) / sin (22.5°)   

h = (1/2) cot (22.5°) ≈ 1.207

Area =  8 (1/2) (1) (1.207)  ≈  4.828

The area of the octagon is 4*sqrt(2) + 4.

We cut a regular octagon ABCDEFGH out of a piece of cardboard.    

If $AB = 1$, then what is the area of the octagon?    

There's a formula for the area of a regular octagon in terms of its side "s" 

A  =  2s² • (1 + sqrt(2))    

A  =  (2)(1²)(1 + 1.414)    

A  =  (2)(2.414)    

A  =  4.828     same as Chris ... I knew it would be.    

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