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What is the size of a diagonal line of a continuous hexagon with side length

?

Explanation:

Regular hexagons are comprised of six equilateral triangles; in our question, these triangles each have side size 4 (see diagram).

You are watching: How many diagonals are there in a hexagon

The size of a diagonal is same to two times the size of the side. In this instance, the answer is 8.

Explanation:

A diagonal line is a heat segment joining two non-adjacent vertices that a polygon. A constant hexagon has six sides and six vertices. One vertex has actually three diagonals, for this reason a hexagon would have actually three diagonals times 6 vertices, or 18 diagonals. Division this number through 2 to account for duplicate diagonals in between two vertices. The formula for the variety of vertices in a polygon is:

where

.

Explanation:

A diagonal line connects 2 non-consecutive vertices the a polygon. A hexagon has actually six sides. There space 3 diagonals from a solitary vertex, and there are 6 vertices on a hexagon, which suggests there would certainly be 18 diagonals in a hexagon. However, we need to divide by 2 as half of the diagonals are usual to the exact same vertices. Thus there room 9 distinctive diagonals in a hexagon. The formula for the number of diagonals the a polygon is:

where n = the variety of sides in the polygon.

Thus a pentagon thas 5 diagonals. One octagon has actually 20 diagonals.

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