SOLUTION: hi, i would like to know the area of a regular heptagon who's perimeter is 1000m. can you please help me and answer this question. thanks bye!

Algebra ->  Surface-area -> SOLUTION: hi, i would like to know the area of a regular heptagon who's perimeter is 1000m. can you please help me and answer this question. thanks bye!      Log On


   

Question 91325: hi, i would like to know the area of a regular heptagon who's perimeter is 1000m.
can you please help me and answer this question.
thanks
bye!
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Heptagon has 7 sides.
Draw the picture including the 7 interior triangles.
Each side is 1000/7 = 142.86
A central angle of one of the interior triangles is 360/7 = 51.43 degrees
Draw an altitude from the center to one of the sides. That bisects the
side.
Find the altitude using tan(51.43/2)=71.43/altitude
altitude = 148.32
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Area of one of the 7 interior triangles is 71.43*148.32 = 10594.58
Area of the whole heptagon = 7*10594.58 = 74162.08 sq meters
Cheers,
Stan H.