The given polygon has 10 sides
The length of one side = 12
For the shown right triangle
Base = 12/2 = 6
And the central angle =
[tex]\frac{360}{10}=36[/tex]
so, the opposite angle to the base of the triangle = 36/2 = 18
So, the other acute angle = 90 - 18 = 72
Let the length of the apothem = A
using the sine rule:
[tex]\begin{gathered} \frac{A}{\sin72}=\frac{6}{\sin 18} \\ \\ A=6\cdot\frac{\sin 72}{\sin 18}=18.466 \end{gathered}[/tex]
Rounding to the nearest hundredths
So, the answer will be Apothem = 18.47
