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Regular Decagon Area and Geometry — result sheet
Calculate the area, perimeter, apothem, circumradius, and interior angle of a regular decagon from its side length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: For n = 10, perimeter P = 10s; apothem a = s/(2 tan(π/10)); area A = ½aP; circumradius R = s/(2 sin(π/10)); each interior angle = 144°.
A regular decagon is a ten-sided polygon with equal sides and equal angles. Its center-to-side apothem splits the shape into ten equal triangles, which makes the area auditable rather than treating the decagon as an arbitrary outline.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Equal side length — length units; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Equal side length | 5 |
Area ≈192.3552 square units; perimeter =50; apothem ≈7.6942; circumradius ≈8.0902; interior angle =144°.
Assumptions and limits
- The decagon is regular: all ten sides and all ten interior angles are equal.
- The side length is positive and every length uses one consistent unit.
- The polygon is planar and Euclidean.
- Area uses square length units and radii use length units.
- The tool does not calculate an irregular decagon from ten separate vertices.
- Rounding is applied only to displayed values.
- A real manufactured shape may have tolerances that are not represented by the ideal formula.
- Keep the side unit attached when comparing the result with a drawing or plan.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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