Expert: Paul Klarreich - 12/15/2007

Question
what is the area of a pentagon if the perimeter is 1000 meter, please can you include the working out... thanks

Answer
Questioner:   george
Category:  Advanced Math
Private:  No
 
Subject:  fence cw
Question:  what is the area of a pentagon if the perimeter is 1000 meter, please can you include the working out... thanks
 
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HI, George,

Start by drawing your pentagon.  VERY LARGE.  Now call the center O, and vertices ABCDE.  Draw OA, OB, etc.  
Now look only at triangle OAB.  Draw the altitude from O to the midpt M of AB, call this h.

Each angle of the pentagon is 108 deg, so <OAB = 54 deg, and AM = 100 meters.  Now write:

tan 54 = h/100.

Use your calculator to find h.
DEtermine the area of triangle OAB = 1/2 base * height = 1/2 (200) h.
Multiply by 5.