How many vertices does a hexagon have?

What is a hexagon in mathematics?

A hexagon is a geometric figure with six sides and six vertices. It can be regular or irregular. A regular hexagon is a convex hexagon whose six sides all have the same length and whose internal angles measure 120 degrees.

Beyond its basic characteristics, the hexagon has many other interesting properties. For example, it can be inscribed in a circle, with each vertex touching the circle. This circle is called the circumscribed circle, and its center is the point of intersection of the bisectors of the hexagon’s sides.

The area of a regular hexagon can be calculated using the following formula: area = 3 × side² × √3 / 2. This formula determines the area of the hexagon as a function of the length of its sides.

A hexagon can also be subdivided into equilateral triangles, where each interior angle measures 60 degrees. The sum of the interior angles of a hexagon is 720 degrees, which is only true if the hexagon is convex.

The diagonals of a hexagon can be calculated by multiplying the length of a side by two, or by using the formula: diagonal = side × √3. These diagonals connect non-adjacent vertices of the hexagon.

A hexagon can also be used to form other geometric shapes such as triangles, parallelograms, rectangles and rhombuses. For example, by connecting the hexagon’s vertices with segments of equal length, it’s possible to construct a regular octagon.

Hexagons also have axes of symmetry. These axes are straight lines that divide the hexagon into two symmetrical parts. A regular hexagon has six axes of symmetry, corresponding to the number of sides.

Using the principles of geometry, you can construct a hexagon using tools such as the compass, ruler and square. What’s more, by knowing the angle measures or the length of at least one side or diagonal, you can calculate the side lengths and angle measures of a hexagon.

The hexagon is a common and versatile geometric figure, used in a wide range of applications. Its properties and its ability to form other shapes make it an important object of study in geometry. What’s more, it offers numerous possibilities for geometric calculations and is used in a variety of practical applications. All in all, the hexagon is a fascinating geometrical figure that arouses the interest of mathematicians and researchers alike.