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Q:

# How many diagonals does a hexagon have?

A:

A hexagon has nine diagonals regardless of whether it is a regular or irregular polygon. This can be determined by utilizing a simple formula that applies to polygons with any number of sides.

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When used in reference to polygons, a diagonal is a line segment that can be connected from any one vertex to another that isn't already directly connected to it. Since each vertex is already connected to itself and the two directly beside it, diagonals can be drawn to the number of vertices in the polygon save three. This number is then multiplied by the number of vertices and divided by two to account for each line segment having two end points. Thus the formula n(n-3)/2, where "n" is the number of vertices, can be used to determine the number of diagonals in a given polygon.

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## Related Questions

• A:

A triangle has zero diagonals. Diagonals must be created across vertices in a polygon, but the vertices must not be adjacent to one another. A triangle has only adjacent vertices.

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• A:

A pentagon has five diagonals on the inside of the shape. The diagonals of any polygon can be calculated using the formula n*(n-3)/2, where "n" is the number of sides. In the case of a pentagon, which "n" will be 5, the formula as expected is equal to 5.

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• A:

A dodecagon, a polygon with 12 sides and 12 vertices, has 54 distinct diagonals. The formula for determining the number of diagonals of an n-sided polygon is n(n - 3)/2; thus, a dodecagon has 12(12 - 3)/2 = 12(9)/2 = 108/2 = 54 diagonals.