Question

O is the center of the regular hexagon below. Find its perimeter. Round to the nearest tenth if necessary.

Answer 1

To solve this problem, we have to find the side length and multiply it by the number of sides of the figure.

To find the length side we will use the following formula:

`ap=\sqrt[]{I^2-(\frac{I^{}}{2})^2}\text{.}`

Where ap is the length of the apothem, and I is the side length.

Substituting the given values, we get:

`10=\sqrt[]{I^2-((I)/(2))^2}.`

Solving the equation for I, we get:

`\begin{gathered} \\ I=\frac{2*10}{\sqrt[]{3}}. \end{gathered}`

Therefore, the perimeter of the hexagon is:

`6I=6*\frac{2*10}{\sqrt[]{3}}\approx69.3\text{ units.}`

Answer:

`69.3\text{ units.}`