An artist uses a regular decagon to make a frame. If the side is 12 cm, what's the total border length?
120 cm
A decagon is a ten-sided polygon, and "regular" means all ten sides are of equal length.
The border of the frame is simply the boundary of this polygon, i.e. its perimeter.
For any regular polygon the perimeter is \(P = n\times s\), where \(n\) is the number of sides and \(s\) the length of one side.
Here \(n = 10\) and \(s = 12\) cm.
Substituting, \(P = 10\times 12\).
This evaluates to \(P = 120\) cm.
The key idea is that a regular polygon's perimeter is just its side length repeated once for every side.
The total border length of the frame is 120 cm.
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