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Decagon Area Calculator

Work out decagon area instantly with clear inputs, formula shown and shareable results.

About Decagon Area Calculator

A regular decagon has 10 equal sides. Splitting it into 10 isosceles triangles from the centre gives A = 10s² / (4·tan(π/10)), which evaluates to (5/2)·cot(π/10)·s² ≈ 7.694209·s².

Formulas

Area

A = 10s² / (4·tan(π/10)) = (5/2)·cot(π/10)·s² ≈ 7.694209·s²

Apothem

a = s / (2·tan(π/10))

Worked example

With the default values below, Decagon Area Calculator returns Area of one decagon of 276.9915. Change any input above and every figure here is recalculated in your browser.

Inputs used

Side lengthminimum 0
6
Number of shapesminimum 1
1

Results

Area of one decagon
276.9915
Perimeter
60.0000
Apothem
9.2331
Total area of all shapes
276.9915

Step by step

  1. 1Values used
  2. 2Area
  3. 3Apothem
  4. 4Area of one decagon= 276.9915
  5. 5Perimeter= 60.0000
  6. 6Apothem= 9.2331
  7. 7Total area of all shapes= 276.9915

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the interior angle of a regular decagon?

(10 − 2) × 180° / 10 = 144°.

Does the formula need a regular decagon?

Yes. For an irregular decagon use the shoelace formula on its vertex coordinates instead.

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