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

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.