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# Apothem problem

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I have a pentagon with side length 7, and I need to know the area. Any help?

liveevillevi  Apr 19, 2017

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+6536
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area of pentagon = 10 * area of third triangle

area of third triangle = (1/2) * base * height

area of third triangle = (1/2) * 3.5 * (3.5 / tan 36º)

area of third triangle = 6.125 / tan 36º

area of pentagon = 10 * 6.125 / tan 36º

area of pentagon = 61.25 / tan 36º

area of pentagon ≈ 84.303 square units

*edit*

as long as this is a regular pentagon! :)

hectictar  Apr 19, 2017
edited by hectictar  Apr 19, 2017
Sort:

#1
+6536
+2

area of pentagon = 10 * area of third triangle

area of third triangle = (1/2) * base * height

area of third triangle = (1/2) * 3.5 * (3.5 / tan 36º)

area of third triangle = 6.125 / tan 36º

area of pentagon = 10 * 6.125 / tan 36º

area of pentagon = 61.25 / tan 36º

area of pentagon ≈ 84.303 square units

*edit*

as long as this is a regular pentagon! :)

hectictar  Apr 19, 2017
edited by hectictar  Apr 19, 2017

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