SOLUTION: Find the area of a regular pentagon with apothem 15 meters. Show all work to receive credit.

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Question 111917: Find the area of a regular pentagon with apothem 15 meters. Show all work to receive credit.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
apothem=r=15 m
n=5
beta=180(n-2)/n=180*3/5=108 deg=each interior angle.
R, the radius of a circumscribed circle bisects each int angle.
cot(54)=adj/opp
adj=cot(54)*r=cot(54)*15=10.098...
10.098...*2=21.796...=base of the triangle and a side of the pentagon
1/2alt.*base=A
1/2*15*21.796...=163.472... m^2
There are 5 triangles in the regular pentagon.
5*163.472...=817.36...m^2 area of the pentagon.
Ed