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Q:

# How many diagonals does a decagon have?

A:

A decagon has 35 diagonals regardless of whether it is a regular or irregular polygon. This can be determined by using a simple formula that applies to polygons with any number of sides.

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A diagonal, when used in reference to polygons, is a term used to describe the number of line segments that can be connected from any one vertex to another that is already attached 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 minus 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, calculates the number of diagonals in any given polygon.

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## Related Questions

• A:

A heptagon has 14 diagonals. In geometry, a diagonal refers to a side joining nonadjacent vertices in a closed plane figure known as a polygon. The formula for calculating the number of diagonals for any polygon is given as: n (n - 3) / 2, where n is the number of vertices of the polygon.

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• 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:

An octagon has 20 diagonals. A shape's diagonals are determined by counting its number of sides, subtracting three and multiplying that number by the original number of sides. This number is then divided by two to equal the number of diagonals.