Question

What is the length of the apothem of a regular hexagon with 10-cm sides?

Answer 1

Answer:

The length of apothem of given hexagon is 8.66 cm

Step-by-step explanation:

Apothem of a polygon is given by:

$apothem = \frac{s}{2\ tan\ (\frac{180}{n})}$

Here

s is length of side

tan is trigonometric function

and n denotes number of sides

Given that the polygon is a hexagon

$s = 10cm\\n = 6$

Putting the values in the formula

$apothem = \frac{10}{2\ tan\ (\frac{180}{6})}\\= \frac{10}{2\ tan\ 30}\\=\frac{10}{2 * 0.5773}\\=\frac{10}{1.1546}\\=8.6610\\Rounding\ off\ to\ nearest\ hundredth\\= 8.66\ cm$

Hence,

The length of apothem of given hexagon is 8.66 cm