If you're stuck solving geometry problems involving polygons, this hexagon calculator will surely be of use to you. Apart from a handy hexagon area formula and perimeter formula, it will also help you in calculating the lengths of its diagonals and the radii or an inscribed and circumscribed circle. Stop wondering what are the internal angles equal to, or how to find the area of a hexagon, and solve those pesky math problems in no time!
Properties of a regular hexagon
A regular hexagon, just like an octagon, is a geometric figure called a polygon. It has six edges of equal length. The internal angle at each of the six vertices measures exactly 120°. The total number of hexagon's diagonals is equal to 9 - three of these are long diagonals that cross the central point, and the other six are also called the "height" of the hexagon.
The easiest way to construct a regular hexagon is by drawing six equilateral triangles that all have a common vertex in the central point of the hexagon.
How to find the area of a hexagon?
Calculating the area of the hexagon is very simple. The general idea is to calculate the areas of the six triangles that the hexagon is comprised of and adding them together.
The length of a hexagon's edge - and consequently, also the length of a triangle's edge - is called a. Then, we can express the area of one triangle as:
A₀ = a * h / 2 = a * √3/2 * a / 2 = √3/4 * a²
After multiplying this area by six, we get the hexagon area formula:
A = 6 * A₀ = 6 * √3/4 * a²
A = 3 * √3/2 * a²
Of course, you don't have to perform these calculations manually - just plug the edge length into the hexagon calculator and watch it determine the area for you!
How to find the perimeter of a hexagon
Calculating the perimeter of a hexagon is even simpler than finding its area. All you have to do is add the lengths of all six edges. As they are equal in length, the equation for the perimeter of a hexagon is as follows:
P = 6 * a
Diagonals of a hexagon
Our hexagon calculator can also spare you some tedious calculations while determining the lengths of the hexagon's diagonals. There are two types of these diagonals:
- Long diagonals - they always cross the central point of the hexagon. As you can notice from the picture above, the length of such a diagonal is equal to two edge lengths:
D = 2a.
- Short diagonals - also called the height of the triangle, these diagonals do not cross the central point. Their length is equal to
d = √3 * a.
Circumradius and inradius
The last two values that our hexagon calculator can easily find are the radii of a circumscribed and an inscribed circle.
- Circumradius: to find the radius of a circle circumscribed on the regular hexagon, you need to determine the distance between the central point of the hexagon (that is also the center of the circle) and any of the vertices. It is simply equal to
R = a.
- Inradius: the radius of a circle inscribed in the regular hexagon is equal to a half of its height:
r = √3/2 * a.