How do you calculate the area of a regular hexagon? How do you calculate the area of a regular hexag

A regular hexagon with a side length.

Its area is the area of 6 regular triangles with a side length a.

The sum is calculated as s=(3 3 2)a 2.

First, divide the regular hexagon into six identical triangles through the center, then only take the area of each regular triangle, and then multiply it by six, which is the area of the regular hexagon.

When calculating the area of a triangle, using the Pythagorean theorem, it can be found that the area of a regular triangle with a side length is 3 4 a. This area is then multiplied by six to give the area of the regular hexagon as (3 2) 3a

Therefore, the formula for the area of a regular hexagon = (3 2) 3a (where a is the length of the sides of the regular hexagon).

Solution: A regular hexagon can be mistaken for the sum of the areas of six regular triangles.

Just multiply the area of one by 6.

When finding the area, you should use a circumscribed circle with multiple deformations to connect the center of the circle and the corners, so that you can find the area of one of the triangles.

Let the side length be a, and she consists of 6 equilateral triangles.

The area of each triangle is: (a*a*(3) 2) 2

Hexagon s = 6 * a*a*(3) 2) 2= 3*3 2*a*a

Divided into 6 equilateral triangles, let the side length of the regular hexagon be a, then the area of the regular hexagon is 3 3 2a

Let the side length of the regular hexagon be a=r

Regular hexagon area = 6 3r 4

3√3r²/2

Or. 3√3a²／2

How do you calculate the area of a regular hexagon? Master this calculation formula, this kind of problem is oral arithmetic problem!

The formula for the area of the hexagonal leaning rock is: (root number 3) 4*a*a*6 = root number 3)*3 2*a*a

If the side length of the regular hexagon is a, connect the six vertices of the hexagon with the center of the hexagon and divide it into six regular triangles with the side length of a.

The formula for the area of a regular triangle is: (root number 3) 4*a*a Therefore, the formula for the area of a hexagon is: (root number 3) 4*a*a*6 = root number 3)*3 2*a*a

In plane geometry, a regular hexagon is a polygon with six equal sides and six equal interior angles. The inner angles are equal and the hexagons are equal.

The area of a regular hexagon with a side length is the sum of the areas of 6 regular triangles with a side length a, and the formula is s=(3 3 2)a 2

Because a regular hexagon is made up of six equilateral triangles, so:

Area of the regular hexagon = area of the triangle 6 = The height of these equilateral triangles is the radius of the inscribed circle of the regular hexagon, i.e.: 3 2 a

A hexagon is a type of polygon, which refers to all polygons that have six sides and six corners. A regular hexagon can be drawn with a compass ruler alone. Because when a regular hexagon is attached to a circle, the radius of the circle is just equal to the length of the sides of the regular hexagon, and the longest diagonal of the regular hexagon is equal to the diameter of the circle.

In ancient China, there was a saying that the relationship between the circumference and the diameter of the circle was "one diameter on three days", which can be regarded as the result of using a regular hexagon as an approximate figure for a circle.

Method 1: Make a circle, take the radius as the length unit to make a bend (the radius is the side length of the regular hexagon), divide the circle, and connect the points, that is, the regular hexagon.

Method 2: Draw a line segment ab of any length. Take a as the center of the circle and ab as the radius to make the circle a.

With B as the center of the circle and AB as the radius, the circle B and the circle A intersect at the point C. Connect AC and BC. The triangle ABC is equilateral and three-only boring angles.

Take the third divide point M on AB. Take the dots n and o on ac and bc respectively so that cn=am=ob. Make MX parallel to BC and AC to point X.

Make ny parallel to ba, and cross bc to point y. Make oz parallel to ac, cross ab at point z. then nyozmx is a regular hexagon.

Method 3: Draw a circle and make one of its diameters. Take the two endpoints of the diameter as the center of the circle, draw the circle with the radius of the circle as the radius, make 4 intersection points, and connect the 4 points and the two endpoints of the diameter in order.

0 in the middle of the regular hexagon, cross 0 to make the perpendicular line of any side of the regular hexagon, and then multiply the length of this side by the length of the perpendicular line to get a number to divide the number by 2 and then multiply by 6.

The area of a regular hexagon is (3 2) 3a (where a is the length of the side).

Whether it is a regular hexagon or an irregular hexagon, there are many ways to calculate its area, you can refer to the following steps.

If the edge length is known, you can write the formula for solving the area directly. Since a regular hexagon is made up of six equilateral triangles, the solution formula can be derived from the equilateral triangle area formula.

Determines the side length of the regular hexagon. If the edge length is known, write it directly, for example, the side length here is 9cm. If the length of the side is unknown, but the perimeter or centroid distance (the height on one side of the triangle that makes up a regular hexagon), you can also find the edge length by:

If the perimeter is known, divide it by six to get the edge length. If the circumference of a hexagonal rock shape is 54cm, divide it by six to get 9cm, which is the side length.

If you only know the side center distance, you can multiply the resulting value by two by taking in the formula a = x 3. This is because the edge centroid is represented in a triangle of 30-60-90° x 3 sides. For example, if the distance between the sides is 10 3, then the side length should be 10*2, which is 20.

Brings the value of the edge length into the formula. When you have an edge length of 9, bring 9 into the original formula, like this: Area = 3 3 x 92) 2

Simplify the answerFind the solution of the equation and write the answer. Since you're solving for an area, you should write the unit as squared.

The regular hexagon area is calculated from the known edge centroid distance

Write out the formula for solving the area of a regular hexagon based on the distance between the sides and centers. The formula is: Area = 1 2 x Perimeter x Perimeter x Perimeter Distance.

Bring in the edge centroid value.

Use the edge of the heart distance to find the circumference.

Bring all known quantities into the formula. Finding the girth is the hardest step. Now you just need to bring the centroid distance and perimeter into the equation and solve it:

Area = 1 2 x perimeter x side centrium.

Area = 1 2 x 60 cm x 5 3 cm

Simplify the answerThe expression of the result is simplified until free radicals are completely eliminated. Don't forget to make the final answer square so that it is virtual.

Because it is a regular hexagon, the regular hexagon can be divided into 6 congruent triangles through the center, and the height of the regular triangle can be found by using the Pythagorean theorem to be 3 2 a, and the area of each triangle is 3 4 a, so the area of the regular hexagon is (3 2) 3a (where a is the side length).

Regular Polygon Properties:

1. All vertices of a regular polygon are on the same circumscribed circle, and each regular polygon has an inscribed circle.

2. Regular polygons can be graphed with rulers and rulers, and only if the odd prime factor of the number of sides n of the regular polygon is the Fermat number. See polygons that can be drawn with a ruler.

3. Inner corners. The internal angles and degrees of a regular n-sided are: (n 2) 180°, and one of the internal angles of a regular n-sided is (n 2) 180° n.

4. an outer corner. The sum of the outer angles of the regular n-sided is equal to n·180° (n 2)·180° 360°, so one of the outer angles of the regular n-sided is: 360° n, so one of the inner angles of the regular n-sided can also be used with this formula:

180°－360°÷n。

The area of a regular hexagon with a side length is the sum of the areas of 6 regular triangles with a side length a, and the formula is s=(3 3 2)a 2