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Idiotinabox
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Homework Statement
The question says that there is a square that has a side of length 1cm. It then says 4 equal triangles are cut, one off each corner. The resulting shape is a regular octagon. What is its area?
Homework Equations
I believe the sides of the triangles to both be (1-x)/2 assuming we let each side of the octagon be length x. This means that length x is represented by (triangle side length)^2 + (triangle side length)^2 = x^2.
The Attempt at a Solution
I essentially let the above equations equal and I get...
(0.5 - x^2/2)^2 + (0.5 - x^2/2)^2 = x^2
Using quadratic after simplifying the above...
X= rt2 - 1
From there I let that equal x again. I find the total area of all 4 triangles and get 1- area of four triangles which leaves me with 0.828cm^2
Is this correct? I'm not convinced it is actually correct. Any guidance?