Number of Diagonals
Geometry
Level
2
For a regular polygon with number of sides n, how many diagonals can be drawn?
n(6-n)
(10n)/2
(n(n-3))/2
6n-5
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1 solution
If n sides, so n vertices.
Each vertex is linked to n-3 vertices (n vertices less itself, and less 2 consecutive vertices).
n-3 diagonal segments, multiplied by n vertices.
Then divide by 2, because each segment [AB] is [BA], so they were counted exactly twice.