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

Question

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

amistre64 · Answer

an octagon has 8 sides, so...64/8 = 8 feet for each side.

amistre64 · Answer

each section consists of  triangle with a base of 8 and a 45degree angle...

amistre64 · Answer

and 2 other angles at 67.5 degrees....

anonymous · Answer

so a?

amistre64 · Answer

dunno yet, I havent worked it out that far :)

amistre64 · Answer

if we use the law of sines; then h= 4sin(67.5)/sin(22.5)...

amistre64 · Answer

calculator says h = 9.65685

Area = about 309.019  ?  is that an option?

amistre64 · Answer

yeah, go with (a)  :)

anonymous · Answer

thank you