Question

Please help and thank you

Answer 1

Answer:

A. $11\frac{5}{8}\textrm{ inches}$

Step-by-step explanation:

Given:

The regular polygon is a decagon having 10 sides.

Perimeter of the given polygon is,

$P=116\frac{1}{4}\textrm{ inches}=116.25\textrm{ inches}$.

We know that, perimeter of a regular polygon of $n$ sides is given as,

$P=na$ where, $a$ is the length of each side.

Here, $n=10,P=116\frac{1}{4}\textrm{ in}$

Plug in these values and solve for $a$. This gives,

$P=na\\116\frac{1}{4}=10a\\116.25=10a\\a=\frac{116.25}{10}=11.625=11+\frac{625}{1000}=11+\frac{5}{8}=11\frac{5}{8}\textrm{ in}$

Therefore, the side length of the given polygon is $11\frac{5}{8}\textrm{ inches}$