There are several diagonals in the 8 sided polygon

There are a total of 8 vertices in an 8-sided polygon, and from a certain vertex, in addition to this vertex and the two adjacent vertices, there are 8-1-2 5 vertices, which can be used to connect diagonals.

A total of 8x (8-1-2) kinds of continuous methods; But the two points share a line segment, and each diagonal is drawn repeatedly, so there are a total of diagonals 8x(8-1-2) 2=20.

As to how many diagonals there are in an n-side, we can reason about a formula.

First, let's give an example to understand it briefly: triangles.

There are 0 strips, quadrilateral.

There are 2, there are 5 pentagons, there are 5 vertices in the pentagon, starting from a certain vertex, in addition to this vertex, and the adjacent two vertices, there are 5-1-2 2 vertices, which can be used to connect diagonals, a total of 5x(5-1-2) kinds of conjunctions; But the two points share a line segment, and each diagonal is drawn repeatedly, so there are a total of diagonals 5x(5-1-2) 2=5.

2. Reason out a general formula: if it is an n-sided shape, the total number of diagonal lines: n(n-3) 2, and the reasoning process can replace 5 with n in the above pentagon example, without repeating it.

The 8-sided has a total of (8-3) 8 2 = 20 diagonals.

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The 8-sided polygon has a total of 20 diagonals. There are a total of 8 vertices in the 8-sided polygon, starting from a certain vertex, in addition to this vertex, and the two adjacent vertices, there are 8-1-2 5 vertices, which can be used to connect diagonals, a total of 8x (8-1-2) kinds of conjunctions; But the two points share a line segment, and each diagonal is drawn repeatedly, so there are a total of diagonals 8x(8-1-2) 2=20.

An octagon is a kind of figure in mathematics, which is a closed figure surrounded by eight line segments connected end to end, and it has eight sides and eight corners. Octagons can be divided into regular octagons and non-regular octagons. The sum of the inner angles of the octagon is 1080 degrees, and the sum of the outer angles is 360 degrees.

Eight lines of equal length, each with an inner angle of 135°, are connected end to end to form a closed shape of a flat figure called a regular octagon. Each corner of a regular octagon is equal in size and each edge is equal in length. An octagon that is not a regular octagon is called a non-regular octagon.

From one of the vertices of the n-side, there are a total of n-3 diagonals.

Therefore, starting from the collapse of one of the vertices of the 8-sided shape, the barrage has 5 diagonal simple cover transports.

Eight vertices, starting from each vertex, in addition to itself and the two adjacent vertices, there are 5 vertices that can be connected.

For example, the manuscript: beetles, butterflies, snails, key code rolling five poisons, etc., because of the meaning of these small insects, carvers use the color difference of jade mold. Five poisons: refers to the five animals of centipedes, toads, snakes, cockroaches, and scorpions.

Starting from a top hunger core point in the octagon, there are a total of 20 diagonals.

Because each vertex has 5 diagonals, 5*8) 2=20 (strips).

So, there are a total of 20 diagonals.

The octagon has eight corners, so from one vertex there are two corners next to each other, so there are five corners that make up five diagonals.

The number of diagonals of an n-sided is the product of the difference between n and n minus 3, divided by 2. When the figure is hexagonal, n is equal to 6, so the number of diagonals of the hexagon is equal to the product of the difference between 6 and 6 minus 3 and divided by 2, which is equal to 9. That is, there are 9 hexagonal diagonals.

What is a regular hexagonA regular hexagon is a polygon with six equal sides and six equal interior angles in plane geometry. The inner angles are equal and the hexagons are equal. From the sum of the outer angles of the polygon equal to 360 degrees, an inner angle is 180-(360 6) = 120 degrees, so each inner angle is 120 degrees.

Because it is a regular hexagon, the regular hexagon can be divided into 6 congruent triangles through the center, making the height of the regular triangle, using the Pythagorean theorem to find the height of the free branch chain 3 2 a, the overlapping area of each triangle is 3 4 a, so the area of the regular hexagon is (3 2) 3a.

Each vertex has 5 diagonal trace lines and thread keys.

8 points are 8 * 5 = 40 posture missing, but half of them are double-counted, so.

A total of 20 diagonals.