anonymous
  • anonymous
Somebody Please Help Me A large gazebo is shaped like a regular octagon. it has sides of length 12 feet and an area of about 696 ft^2. Find the area of a similar gazebo that has a perimeter of 64 feet. a) 309.3 ft^2 b) 130.5ft^2 c)261ft^2 d) 116ft^2 e) 1566ft^2
Mathematics
schrodinger
  • schrodinger
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amistre64
  • amistre64
an octagon has 8 sides, so...64/8 = 8 feet for each side.
amistre64
  • amistre64
each section consists of triangle with a base of 8 and a 45degree angle...
amistre64
  • amistre64
and 2 other angles at 67.5 degrees....

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anonymous
  • anonymous
so a?
amistre64
  • amistre64
dunno yet, I havent worked it out that far :)
amistre64
  • amistre64
if we use the law of sines; then h= 4sin(67.5)/sin(22.5)...
amistre64
  • amistre64
calculator says h = 9.65685 Area = about 309.019 ? is that an option?
amistre64
  • amistre64
yeah, go with (a) :)
anonymous
  • anonymous
thank you

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