calculate the perimeter of the polygon

[bumblebee123]

Question: the diagram shows a 12-sided polygon. The area of the polygon is 192cm^2. Calculate the perimeter of the polygon ( to 3.s.f. )

Can anyone help me make a start, I've been attempting it for ages!

 

[ksdhart2]

You refer to "the diagram," but no such diagram/picture is included. Without seeing this diagram, the only way I can see this problem as being solvable is to assume that we're dealing with a regular dodecagon. If that's the case, I'd suggest consulting your textbook/class notes to see if you have a nice formula for the area of a regular polygon. Alternatively, you may want to look it up in an online resource. I found one here, which states:

\(\displaystyle A = \frac{1}{4}ns^2 \cot \left( \frac{\pi}{n} \right)\)

where \(n\) is the number of sides and \(s\) is the length of a side. Plugging in the given information we have:

\(\displaystyle 192 = \frac{1}{4} \cdot 12s^2 \cot \left( \frac{\pi}{12} \right) \\ 192 = 3s^2(2 + \sqrt{3})\)
Where does this lead you?