Question

O is the center of the regular nonagon below. Find its perimeter. Round to the nearest tenth if necessary.
17
O

Answer 1

The perimeter of a nonagon is the sum of its side lengths

The perimeter of the regular nonagon is 840.7 units

How to determine the perimeter

The in-radius of the regular nonagon is given as:

r =17

The perimeter is then calculated as:

$P = \frac{18r}{\tan(pi/9)}$

Substitute 17 for r

$P = \frac{18 * 17}{\tan(pi/9)}$

Evaluate the product of 18 and 17

$P = \frac{306}{\tan(pi/9)}$

Evaluate the quotient

$P =840.7$

Hence, the perimeter of the regular nonagon is 840.7 units

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