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.

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) (Show Source): You can put this solution on YOUR website!

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

Then the area of the octagon is

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