A nonagon, or enneagon, is a polygon with nine sides and nine vertices, and it has 27 distinct diagonals. The formula for determining the number of diagonals of an n-sided polygon is n(n - 3)/2; thus, a nonagon has 9(9 - 3)/2 = 9(6)/2 = 54/2 = 27 diagonals.
The diagonal of a polygon is any line segment joining two nonadjacent vertices. A nonagon has nine vertices, and each vertex has six other vertices that are not adjacent; thus, each vertex forms six diagonals. For each vertex, there are three fewer diagonals than there are vertices. This is the first part of the procedure for finding the number of diagonals of a polygon: n(n - 3) = 9 x 6 = 54. Each diagonal has two end points, so in order to not count a duplicate diagonal, the final step is to divide 54 by 2, which results in 27 diagonals.
Learn MoreA nine-sided polygon is commonly called a nonagon. This polygon, which has nine edges, or vertices, is also called an enneagon. The term enneagon is preferable, but less popular than the name nonagon because the latter is simpler to spell and pronounce, according to Wolfram MathWorld.
Full Answer >A nine-sided polygon is called a nonagon. Another name for a nine-sided polygon is enneagon. The general accepted names are "n-gon" where n is the number of the sides of the polygon.
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 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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