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8 February, 07:23

Calculate the length of the apothem of a regular polygon. A

regular hexagon is shown. What is the length of the apothem,

rounded to the nearest inch? Recall that in a regular hexagon,

the length of the radius is equal to the length of each side of the

hexagon

10 in.

a

5 in

9 in

11 in

4 in

+5
Answers (1)
  1. 8 February, 07:33
    0
    9 in

    Step-by-step explanation:

    For an n-sided polygon, the length of the apothem is ...

    a = r·cos (180°/n)

    We assume your problem statement is saying the radius is 10 inches. For a hexagon, n=6 and we have ...

    a = (10 in) cos (30°) ≈ 8.66 in

    Rounded to the nearest inch, the apothem is 9 in.
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