a regular hexagon is shown. what is the length of the apothem, rounded to the nearest inch? recall that in a…

Explanation:

Step1: Recall hexagon - apothem relationship

A regular hexagon can be divided into six equilateral triangles. The radius of the hexagon is equal to the side - length of the hexagon. Let the radius (r = 10) in. When we consider half of a side of the hexagon and the apothem and the radius, they form a right - triangle. The side - length of the hexagon (s = 10) in, and half of the side - length (a=\frac{s}{2}=5) in, and the radius (r = 10) in.

Step2: Apply the Pythagorean theorem

In the right - triangle formed by the apothem (h), half of the side of the hexagon, and the radius, by the Pythagorean theorem (h=\sqrt{r^{2}-a^{2}}). Substitute (r = 10) in and (a = 5) in. So (h=\sqrt{10^{2}-5^{2}}=\sqrt{100 - 25}=\sqrt{75}\approx8.66) in.

Step3: Round the result

Rounding (8.66) in to the nearest inch gives (9) in.

Answer:

C. 9 in.