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Hi, I'm having a difficult time understanding a couple of Geometry questions on my homework and I'd really appreciate it if someone could answer them and explain to me how to get the same answer.

Question 1: A regular pentagon has an apothem of 3.2 m and an area of 37.2 m². What is the length of one side of the pentagon?

Question 2: A regular hexagon has perimeter 60 in. What is the hexagon's area?

Please and thank you!

  • Geometry -

    area = 1/2 perimeter * apothem
    37.2 = 1/2 * 3.2p
    p = 23.25
    p=5s, so s=4.65

    p=6s, so s=10
    we have 30-60-90 triangles to form apothems, so
    a = 5*sqrt(3) = 8.66

    area = 1/2 * 8.66 * 60 = 259.8

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