Geometry is a very special branch of mathematics which comprises different shapes and sizes. One needs to be very careful while studying geometry because it is very likely to get confused due to its vast nature. All different geometrical figures have unique properties and theorems of their own. Due to its versatile nature, geometry is that field of mathematics which finds its application in many daily works. It is associated with art, physics, architecture and many other such fields. It is undoubtedly one of the oldest branches known in mathematics. A person who specialises in the field of geometry is also known as geometer. The major concepts of geometry include theorems, points, planes, lines, angles, surfaces and many other such aspects. Modern Geometry not only solves 2D and 3D problems but can comfortably deal with more complex problems. Geometry is mainly of four different types: Euclidean, Non-Euclidean, Analytic and differential geometry. One of the most popular portions of geometry is polygon. There are a variety of polygons namely triangle, quadrilateral, pentagon, hexagon, heptagon and so on. Hexagon is a 2D figure which comprises six different but equal sides, vertices and angles. It consists of 9 different diagonals. Here, we will be discussing the important properties of hexagon. This has been explained very well on Cuemath, a global maths and coding platform for all needy students.
Major fundamentals of Hexagon:
Geometry: The hexahedron constitutes six equivalent sides and angles. It comprises nine diagonals. The summation of all interior angles equals seven hundred and twenty degrees and every individual angle measures one hundred and twenty degrees. The summation of all exterior angles is equivalent to three hundred and sixty degrees whereas each exterior angle measures sixty degrees. The area of the hexahedron is derived by breaking it into six small isosceles triangles. Following this, the area of all the individual triangles is calculated and multiplied by six to get the area of the hexagon which is equivalent to 3√3/2 multiplied by the square of any side’s length. The hexahedron’s perimeter is equivalent to the summation of the length of all the respective sides of the hexagon or six multiplied by the length of any single side.
Symmetry: The hexahedron constitutes six different axes of symmetry. Three of the mentioned axes touch the diagonals conversing the vertices and the remaining three penetrate through the centre of the conversing edges. There is a lot to read regarding this polygon and that information will surely be important enough for any student as well as any teacher who is interested in mathematics. This part of mathematics surely brings out the best in every student and it is very interesting.
Circumcircle: The most significant property of the hexagon is the circumcircle. A regular hexagon consists of six apogees. When they are connected, they result in the formation of a circumcircle. This resulting circle is defined as the circumscribed circle of the hexahedron. The radius equals the line drawn from the centre to any respective vertex of the figure. This radius is also known as the circumradius.
Incircle: Besides the circumcircle, one more circle can be formed inside the hexagon. The discussed circle is the incircle. It is inscribed within the boundaries and is formed from the centre of the fringes of this figure. This radius being discussed is the inradius. The inradius is the result of connecting the centre of the figure with the respective apogees. The respective incircle acts as a tangent for all other corresponding lines of the figure.
Theorem: A very interesting theorem regarding this figure is that its conversing sides run parallel to each other.
Here, we have discussed all the important attributes of the highlighted polygon. These properties have vigorous applications in both coordinate geometry and other important fields like trigonometry. Hexagon is a very important figure with respect to both mathematics and the academic curriculum. Problems on hexagons are asked in all important examinations. Therefore, it is very important to know about this special figure and all its unique characteristics.