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24 September, 07:57

Find the area of a regular decagon with perimeter 100 units. Show all work.

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  1. 24 September, 09:58
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    A regular polygon has ten (10) equal sides (since it is regular).

    We are given with the perimeter value which is 100 units and the perimeter formula is P = 10a

    Solving for a (the side measurement), we have:

    100 = 10a

    a = 100/10

    a = 10

    We can now proceed in solving the area and the formula is shown below:

    Area = 5/2 a√ (5+2√5)

    Area = 5/2 * 10√ (5+2√5)

    Area = 76.94 square units

    The answer is 96.94 square units.
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