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Formulas used
For a regular hexagon with side length \(a\), apothem \(r\), circumradius \(R\), and perimeter \(P=6a\):
- Area from side: \(A = \frac{3\sqrt{3}}{2}a^2\)
- Area from apothem: \(A = 2\sqrt{3}\,r^2\)
- Area from circumradius: \(A = \frac{3\sqrt{3}}{2}R^2\)
- Area from perimeter: \(A = \frac{\sqrt{3}}{24}P^2\)
- Relations: \(R=a\), \(r=\frac{\sqrt{3}}{2}a\)
How to find the area of a regular hexagon
There are four equivalent ways. Pick the one that matches your known measurement and apply the corresponding formula. Relations: R = a and r = (√3/2)a.
- From side (a): A = (3√3/2)a². Square the side and multiply by 3√3/2.
- From apothem (r): A = 2√3·r². Apothem is the inradius from center to a side midpoint.
- From circumradius (R): A = (3√3/2)R². For regular hexagons, R equals the side length.
- From perimeter (P): A = (√3/24)P². Use when the total boundary length is available.
| Given | Value | Formula | Computed area |
|---|---|---|---|
| Side (a) | 2 m | A = (3√3/2)a² | 10.392305 m² |
| Apothem (r) | 1.732051 m | A = 2√3·r² | 10.392305 m² |
| Circumradius (R) | 2.000000 m | A = (3√3/2)R² | 10.392305 m² |
| Perimeter (P) | 12.000000 m | A = (√3/24)P² | 10.392305 m² |
Always convert lengths to consistent units before applying these formulas to avoid unit errors.
the base of a regular pyramid is a hexagon. what is the area of the base of the pyramid?
The base is a regular hexagon, so its area depends only on base dimensions, not on the pyramid’s height or slant height. Use any equivalent hexagon area formula below.
- From side length a: A_b = (3√3/2)a²
- From apothem (inradius) r: A_b = 2√3·r²
- From circumradius R: A_b = (3√3/2)R²
- From perimeter P = 6a: A_b = (√3/24)P²
| Given | Value | Formula | Base area Ab |
|---|---|---|---|
| Side (a) | 0.400 m | Ab = (3√3/2)a² | 0.415692 m² |
| Apothem (r) | 0.346410 m | Ab = 2√3·r² | 0.415692 m² |
| Circumradius (R) | 0.400 m | Ab = (3√3/2)R² | 0.415692 m² |
| Perimeter (P) | 2.400 m | Ab = (√3/24)P² | 0.415692 m² |
Note: Having only the pyramid’s height (h) or slant height (l) is insufficient to determine the base area without at least one base measure such as a, r, R, or P.
a regular hexagon has a radius of 20 in. what is the approximate area of the hexagon?
For a regular hexagon the circumradius equals the side length: R = a. The area formula becomes A = (3√3/2)R².
- Insert R = 20 in into A = (3√3/2)R².
- A ≈ (3×1.73205/2) × 20² ≈ 2.59808 × 400.
- A ≈ 1039.230 in² (approximately).
| Unit | Approximate area |
|---|---|
| in² | 1039.230 |
| ft² | 7.2169 |
| cm² | 6704.70 |
| m² | 0.6705 |
Result uses R = a and standard conversions: 1 ft² = 144 in², 1 in² = 6.4516 cm², 1 m² = 1550.0031 in².
How to use this calculator
- Select which quantity you know: side, apothem, circumradius, or perimeter.
- Enter its value and choose a length unit.
- Pick the desired output area unit.
- Click Calculate to see area and derived values instantly.
- Use Download CSV or Download PDF to export your results.
Tip: When designing tiling or materials, apothem relates directly to hexagon spacing.
Example data
Illustrative examples with side length as the known value and areas in different units.
| Side (a) | Unit | Area (m²) | Area (cm²) | Area (in²) | Area (ft²) |
|---|
Applications
Use these formulas in flooring layouts, honeycomb structures, RF antenna arrays, and fast material takeoffs where consistent spacing and area precision matter.
Common pitfalls
- Confusing apothem with circumradius; they are not equal.
- Using irregular hexagon sides; all sides and angles must match.
- Forgetting to square the length unit when converting area.