Question

Question: Find the apothem for the following regular figure rounded to the hundredths

Answer 1

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 =

`(360)/(10)=36`

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:

`\begin{gathered} (A)/(\sin72)=(6)/(\sin 18) \\ \\ A=6\cdot(\sin 72)/(\sin 18)=18.466 \end{gathered}`

Rounding to the nearest hundredths

So, the answer will be Apothem = 18.47