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.
Know MoreWhen 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.
Learn more in ShapesA 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.
Full Answer >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.
Full Answer >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.
Full Answer >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.
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