How to find the diagonal length of a regular hexagon knowing the opposite side?

Connect the diagonal lines to form 6 regular triangles, and the length of the opposite side is the side length of the regular triangle, half of the diagonal of the hexagon. The diagonal length is twice as long as the contrast length.

Solution:

The side length is half of the distance between the side of the cat, and there will be an isosceles trapezoidal shape after the drawing, and the bottom angle is just 60 degrees, then it is an equilateral triangle, and the side length of the hexagon is just the middle line of the triangle, that is, half of the distance between the opposite side!

Common Pattern: Snow Crystal.

The hexagonal shape of snow crystals can be subdivided into two categories, one is sheet and the other is columnar. The most beautiful snowflakes that you often see are those six-sided symmetrical flake snow crystals. They usually form at temperatures between -5 degrees Celsius and -20 degrees Celsius, with columnar snowflakes consisting of needle-shaped and hollow columns, needle-shaped snow crystals forming at temperatures between -5 degrees Celsius and hollow columns forming below -20 degrees Celsius.

Solution: The side length is half of the distance between the opposite side, after drawing, there will be an isosceles trapezoidal on the opposite side, and it will be made into an isosceles triangle, and the bottom angle is just 60 degrees, then it is an equilateral triangle, and the side length of the hexagon is just the middle line of the triangle, that is, half of the distance between the opposite side!

Answer 1: Connect two adjacent vertices to get a line segment with a length of the distance from the opposite side, so that it is a; 2. Each angle of the regular hexagon is 120 degrees, and this line segment A divides this angle into 90 degrees and 30 degrees. 3. Therefore, it is to find the right-angled side of the hypotenuse length of the rt triangle of 30 degrees as a 2, and the short right-angled edge is half of the hypotenuse, and set it to x, then (a2) 2+x 2=(2x) 2, after solving x, the hypotenuse is 2x, that is, the side length of the regular hexagon or use a simple method cos30=(a 2) hypotenuse = (3) 2 to solve the hypotenuse = a 3 = (a 3) 3

Join two adjacent vertices to get a line segment of length equal to the distance of the opposite side, so that it is a;

Each angle of a regular hexagon is 120 degrees, and this line segment A divides this angle into 90 degrees and 30 degrees (this should not be explained, right?). )

So it is to find the hypotenuse of the RT triangle of 30 degrees.

The long right-angled edge is a 2, and the short right-angled edge is half of the hypotenuse, so if it is x, then (a 2) 2+x 2=(2x) 2, (it is not difficult for the landlord to solve this, right?) After solving x, the hypotenuse is 2x, which is the side length of the regular hexagon.

Or the easy way.

cos30=(a 2) hypotenuse=( 3) 2 can be solved to get hypotenuse = a 3 =(a 3) 3

Side length = distance to opposite side root number 3

Solution: Because a regular hexagon can be divided into six equilateral triangles that connect vertices with a central point.

So they are diagonal.

It is twice the length of the sides, and each diagonal divides the six triangles of the hexagon into two groups, each group of three equilateral triangles, exactly 60x3=180 is a flat angle, equal to the length of both sides.

A regular hexagon consists of six congruent isosceles triangles; The corresponding central angle of each side is 360° 6 = 60°; The sum of the inner angles of a regular hexagon is: 180° (6 - 2) = 720°, and the sum of the two base angles of the six triangles is exactly the sum of the inner angles of the hexagon, so there is: 720° 2 6) = 60°, which means this.

Summary. Hello dear. Assuming that the hexagon is a regular hexagon, i.e., six vertices evenly spaced over a circle, then every two opposing vertices are a pair of opposite sides, and they are of equal length.

In this case, we can calculate the length of the diagonal using the properties of a regular hexagon. Let the side length of the regular hexagon be a, then the length of the diagonal d can be calculated by the following formula: d = 2a = 2 19 mm cos(30°))mm, where cos(30°) is the cosine value of the inner angle of the regular hexagon.

So, if this hexagon is a regular hexagon and one of the pairs of opposite sides is 19 mm in length, then the diagonal is about mm in length.

Do you know that the opposite side of the hexagon is 19mm, find the diagonal length?

Thank you. Hello dear. Assuming that the hexagon is a regular hexagon, i.e., six vertices evenly spaced over a circle, then every two opposing vertices are a pair of opposite sides, and they are of equal length.

In this case, we can calculate the length of the diagonal macro line using the properties of the six search edges. Let the side length of the regular hexagon be a, then the length of the diagonal d can be calculated by the following formula: d = 2a = 2 19 mm cos(30°))mm, where cos(30°) is the cosine value of the inner angle of the regular hexagon.

So, if this hexagon is a regular hexagon and one of the pairs of opposite sides is 19 mm in length, then the diagonal is about mm in length.

The diagonal length of the regular hexagon is equal to the diameter of its circumscribed circle, and because of the rise and collapse of the hexagonal is divided into six equilateral triangles by the diagonal, the equilateral triangle is noisy and the side length of the hexagon = 19mm, then the diagonal length = 2 The side length of the equilateral triangle = 2 19 = 38mm.

The length of the line = 2 19mm = 38mm, and the length of the diagonal line is 38mm.

Hexagon opposite side 46, how long is the opposite angle, first calculate the side length of the triangle of the equal car Zen wheel, the side of the equal triangle is the side of the regular hexagon, and the two sides on the same straight line are exactly the diagonal of the regular hexagon, so the length of the diagonal in the regular hexagon is 2 times the side length; The closed letter is 46x2 92 diagonally long 92

Summary. Hello, because the sum of the internal angles of a polygon is calculated as: sum of internal angles = n-2)x180°

So the sum of the internal angles of a regular hexagon = 6 - 2) x 180° =4 x 180° =720°

How to calculate the inner angles and side lengths of a regular hexagon.

Hello, because the sum of the internal angles of a polygon is calculated as: sum of internal angles = n-2)x180°, so the sum of the internal angles of a regular hexagon = 6 - 2) x 180° =4 x 180° =720°

Edge length = Perimeter 6

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Hello dear. The sum of the internal angles of a regular hexagon is 180 (6-2)=720°Three diagonals divide the hexagon into 6 congruent triangles, and the width of the hexagon is 39, then the side length of the regular hexagon is 39 2 2 3=, .

Diagonal 2 side length = 2 .

The distance between the opposite sides of a regular hexagon is 39 degrees long, and the diagonal distance is much longer.

Hello! We're happy to answer for you! Hello dear.

The sum of the internal angles of a regular hexagon is 180 (6-2)=720°Three diagonals divide the hexagon into 6 congruent triangles, and the width of the hexagon is 39, then the side length of the regular hexagon is 39 2 2 3=, . Diagonal 2 side length = 2 .

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