Enter any one property of a regular hexagon to calculate the others.
How to Calculate Hexagon Properties
A regular hexagon is a six-sided polygon with all sides equal in length and all interior angles equal to 120°. Understanding how to calculate various properties of a hexagon is essential in geometry, engineering, and many real-world applications. Here's a comprehensive guide on how to perform these calculations:
Hexagon Formulas
The key formulas for calculating hexagon properties are:
Perimeter (P) = 6s
Area (A) = \(\frac{3\sqrt{3}}{2}s^2\)
Apothem (a) = \(\frac{\sqrt{3}}{2}s\)
Circumradius (R) = s
Inradius (r) = Apothem = \(\frac{\sqrt{3}}{2}s\)
Where s is the length of one side of the hexagon.
Calculation Steps
Identify the given property of the hexagon (side length, perimeter, area, or apothem).
If the side length is not given directly, calculate it using the appropriate formula.
Once the side length is known, use the formulas to calculate all other properties.
Round the results to an appropriate number of decimal places if necessary.
Example Calculation
Let's calculate the properties of a hexagon with a side length of 5 units:
Given: s = 5 units
Perimeter: P = 6s = 6 × 5 = 30 units
Area: A = \(\frac{3\sqrt{3}}{2}s^2 = \frac{3\sqrt{3}}{2} \times 5^2 \approx 64.95\) square units
Apothem: a = \(\frac{\sqrt{3}}{2}s = \frac{\sqrt{3}}{2} \times 5 \approx 4.33\) units
Circumradius: R = s = 5 units
Inradius: r = Apothem ≈ 4.33 units
Visual Representation
This diagram illustrates a regular hexagon with its side (s), circumradius (r), and apothem (a) labeled. The hexagon is drawn in blue, the radius in red, and the apothem in green.