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Nonagon Area Calculator

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

About Nonagon Area Calculator

A regular nonagon has 9 equal sides. Splitting it into 9 isosceles triangles from the centre gives A = 9s² / (4·tan(π/9)), which evaluates to (9/4)·cot(π/9)·s² ≈ 6.181824·s².

Formulas

Area

A = 9s² / (4·tan(π/9)) = (9/4)·cot(π/9)·s² ≈ 6.181824·s²

Apothem

a = s / (2·tan(π/9))

Worked example

With the default values below, Nonagon Area Calculator returns Area of one nonagon of 222.5457. 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 nonagon
222.5457
Perimeter
54.0000
Apothem
8.2424
Total area of all shapes
222.5457

Step by step

  1. 1Values used
  2. 2Area
  3. 3Apothem
  4. 4Area of one nonagon= 222.5457
  5. 5Perimeter= 54.0000
  6. 6Apothem= 8.2424
  7. 7Total area of all shapes= 222.5457

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 nonagon?

(9 − 2) × 180° / 9 = 140°.

Does the formula need a regular nonagon?

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

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