SOLUTION: A square with the side length of x has all four corners cut off, forming a regular octagon. Derive the area of the octagon.

Algebra ->  Surface-area -> SOLUTION: A square with the side length of x has all four corners cut off, forming a regular octagon. Derive the area of the octagon.      Log On


   



Question 1104011: A square with the side length of x has all four corners cut off, forming a regular octagon. Derive the area of the octagon.
Answer by greenestamps(13200) About Me  (Show Source):
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Let s be the side length of the regular octagon that is formed. Then the 4 corners that are cut off of the original square can be put together to form a square of side length s; so the area of the 4 corners cut off is s^2; so the area of the octagon is x^2-s^2.

To find the relationship between s and x, observe that
x+=+s%2Fsqrt%282%29%2Bs%2Bs%2Fsqrt%282%29
x+=+s%28sqrt%282%29%2B1%29
s+=+x%2F%28sqrt%282%29%2B1%29+=+x%2A%28sqrt%282%29-1%29

Then the area of the octagon is