Questions on Geometry: Polygons answered by real tutors!

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Question 148550: A regular pentagon can be dissected into 5 isosceles triangles whose vertex angle is at the center of the pentagon. The height of the triangle is 10 cm. find the area of this pentagon.: A regular pentagon can be dissected into 5 isosceles triangles whose vertex angle is at the center of the pentagon. The height of the triangle is 10 cm. find the area of this pentagon.
Answer by mangopeeler07(445) About Me  (Show Source):
You can put this solution on YOUR website!
Pentagon=540 degrees
540/5=108
108=the vertex angle of the isosceles triangle

1/2 of 108=54
tan(54)=x/10
x=13.764
(x=length of half of one side of the pentagon)
2x=27.528

apothem=10
perimeter=137.638

area=1/2ap

137.638(10)=1376.38

1376.38/2=688.19

area=688.19cm^2