SOLUTION: A regular octagon is constructed by cutting off the corners of a square. If each side of the square is 12 cm, then what is the total area, in cm², of the four corners that are cut

Algebra ->  Surface-area -> SOLUTION: A regular octagon is constructed by cutting off the corners of a square. If each side of the square is 12 cm, then what is the total area, in cm², of the four corners that are cut      Log On


   

Question 1147738: A regular octagon is constructed by cutting off the corners of a square. If each side of the square is 12 cm, then what is the total area, in cm², of the four corners that are cut off?
Answer by CubeyThePenguin(3113) About Me  (Show Source):
You can put this solution on YOUR website!
side length of octagon = s

s%2F%28sqrt%282%29%29+%2B+s+%2B+s%2F%28sqrt%282%29%29+=+12
sqrt%282%29+%2A+s+%2B+s+=+12
s%281+%2B+sqrt%282%29%29+=+12
s+=+12%2F%281+%2B+sqrt%282%29%29
s+=+12+%2A+sqrt%282%29+-+12

area of four triangles cut off = 4+%2A+%28%28s%2Fsqrt%282%29%29%5E2%29%2F2+=+s%5E2

s%5E2+=+432+-+288+%2A+sqrt%282%29+=+24.706 cm^2