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Matematika

Obsah pravidelného mnohoúhelníku

Regular Polygon Calculator

Number of Sides
Side Length

What is Regular Polygon Area?

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Kalkulačka oblasti pravidelného mnohoúhelníku vypočítá plochu, obvod a poloměr pro jakýkoli pravidelný mnohoúhelník (stejné strany a úhly) daný délkou strany a počtem stran.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

Vzorec

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f(x)Plocha = (n × s²) / (4 × tan(π/n))

How to Regular Polygon Area

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  1. 1Area = (n × s²) / (4 × tan(π/n))
  2. 2n = number of sides; s = side length
  3. 3Perimeter = n × s
  4. 4Circumradius R = s / (2 × sin(π/n))

Worked Examples

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Example 1
Given:Regular pentagon (5 sides), side 4 cm
Výsledek:Area = (5 × 16) / (4 × tan(36°)) = 80/2.906 = 27.53 cm²

Real-World Applications

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Academic homework and exam preparation

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Engineering and architecture calculations

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Everyday measurement tasks around the home

Regular Polygon Areas (side=1)

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SidesNameAreaInterior angle
3Triangle0.43360°
4Square1.00090°
5Pentagon1.720108°
6Hexagon2.598120°
8Octagon4.828135°
12Dodecagon11.196150°

Frequently Asked Questions

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Q

What is Regular Polygon Area?

A

A regular polygon area calculator computes area, perimeter, and circumradius for any regular polygon (equal sides and angles) given the side length and number of sides. Use this calculator for accurate, instant results.

Q

How accurate is the Regular Polygon Area calculator?

A

The calculator uses the standard published formula for regular polygon area. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

Q

What units does the Regular Polygon Area calculator use?

A

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

Q

What formula does the Regular Polygon Area calculator use?

A

The core formula is: Area = (n × s²) / (4 × tan(π/n)). Each step in the calculation is shown so you can verify the result manually.

Variable Legend

n= number of sidess= side lengthR= circumradiusa= apothem

Area from side length

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Area from circumradius

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Area from apothem

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Deep Dive

Read the full guide on how to use this calculator effectively

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Formula-verified for precision
Reviewed October 2026
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