Hexagon Calculator

Tutorial

What is a hexagon?

A regular hexagon has six equal angles and six equal sides. The measure of each angle is 120⁰. A hexagon has 9 diagonals; three long diagonals pass through the center.

Most important formulas?

The calculator uses the following formulas to find the missing elements of a hexagon.

1. Area

A regular hexagon consists of 6 equilateral triangles. The area of a sing triangle is a²√3/4, so the total area is

A = 6 × a²√3/4 = (3a²√3)/2

Learn how to derive a formula for the hexagonal area.

2. Perimeter

Since a hexagon has six equal sides the perimeter is

A = 6 × a

3. Incircle radius

The incircle radius is equal to the height of a single equilateral triangle so,

r = (a √3)/2

4. Circumcircle radius

The circumcircle radius is equal to the side of a single equilateral triangle so,

R = a

5. Long diagonal

d = 2a

6. Short diagonal

s = a√3

Solved examples

Example 1:

Find the area of a regular hexagon having a side equal to 6 cm.

In the example we will use formula for area of a regular hexagon:

A = (3a²√3)/2
A = (3·6²√3)/2
A = (3· 36√3)/2
A = 3·18√3
A = 54√3

Example 2:

What is the side of the regular hexagon whose short diagonal is s = 12 cm?

In the example we will use short diagonal formula:

s = a × √3
12 = a × √3
a = 12/√3
a = 4√3

Example 3:

Find the side of a regular hexagon, if the area is 24√3.

Again we will start with the formula for the area

A = (3a²√3)/2
24√3 = (3a²√3)/2
2 × 24√3 = 3a^2√3
48√3 = 3a²√3
48 = 3a²
a² = 12
a = √12
a = 2√3