High school Math assist » Geometry » aircraft Geometry » Hexagons » how to discover the length of the diagonal line of a hexagon

What is the length of a diagonal of a continual hexagon v side length

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Explanation:

Regular hexagons are made up of 6 equilateral triangles; in ours question, these triangles each have actually side size 4 (see diagram).

You are watching: Number of diagonals in a hexagon

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The length of a diagonal line is same to 2 times the length of the side. In this instance, the answer is 8.

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Explanation:

A diagonal line is a line segment joining 2 non-adjacent vertices that a polygon. A constant hexagon has six sides and also six vertices. One vertex has three diagonals, for this reason a hexagon would have actually three diagonals times six vertices, or 18 diagonals. Divide this number by 2 come account for duplicate diagonals in between two vertices. The formula because that the number of vertices in a polygon is:

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where

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Explanation:

A diagonal line connects two non-consecutive vertices the a polygon. A hexagon has six sides. There are 3 diagonals indigenous a single vertex, and there are 6 vertices ~ above a hexagon, which suggests there would be 18 diagonals in a hexagon. However, we must divide by 2 as half of the diagonals are usual to the very same vertices. For this reason there are 9 unique diagonals in a hexagon. The formula for the number of diagonals the a polygon is:

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where n = the variety of sides in the polygon.

See more: Animals That Begin With The Letter Q, Animals That Start With Q

Thus a pentagon thas 5 diagonals. An octagon has 20 diagonals.


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