Question

The given figure is a regular hexagon with side length 12 and radius 10. Find the length of the apothem a.Question options:A) 9B) 12C) 15.6D) 8

Answer 1

Okay, here we have this:

We obtain the following triangle:

So, we can see that we obtain a right triangle, considering this we are going to use the Pythagoras theorem:

$10^2=6^2+a^2$

Let's clear "a":

$\begin{gathered} a=\sqrt[]{10^2-6^2} \\ a=\sqrt[]{100-36} \\ a=\sqrt[]{64} \\ a=8 \end{gathered}$

Finally we obtain that the correct answer is the option D.