SOLUTION: We are asked to find the area of a pentagon with all sides being 3 1/4. I have tried everything, please help! (our teacher wants us to find the area and the primeter, I have found

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Question 91769This question is from textbook Prealgebra
: We are asked to find the area of a pentagon with all sides being 3 1/4. I have tried everything, please help! (our teacher wants us to find the area and the primeter, I have found the primeter but can't find the area)
Thanks This question is from textbook Prealgebra

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
find the area of a pentagon with all sides being 3 1/4
Draw the pentagon.
Draw a line segment from the center to each of the vertices.
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One of the central angles is (1/5)*360 = 72 degrees
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Draw an altitude of one of the triangles.
The answer at the denter is (1/2)72 = 36 degrees
the base of the trianble is (1/2)(3 1/4) = (1/2)(13/4) = 13/8
tangent(36) = (13/8) / altitude
altitude = (13/8)/tan36 = 2.2366...
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So area of the triangle is (1/2)(13/8)(2.2366...) = 1.81725... sq units
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There are 10 of these triangles in the pentagon.
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Area of the pentagon = 18.1725 sq units.
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Cheers,
Stan H.