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Decagon calculator

Online calculator and formulas for calculating an decagon, a polygon with 10 vertices

Calculator index

Calculate decagon online


This function calculates various parameters of a decagon.

To perform the calculation, select the required parameter in the menu and enter its value. Then click the 'Calculate' button.


Decagon online calculator

 Input
Argument Type
Value
Decimal places
 Results
Side length a
Perimeter P
Area A
Height h
Diagonal d5
Diagonal d4
Diagonal d3
Diagonal d2
Incircle radius ri
outercircle radius ro
Decagon

Properties

All sides are equal.

All angles are equal.

The bisector and heights all intersect at the center.

Formulas for the equilateral decagon


Area
\(\displaystyle A=\frac{5}{2} · \sqrt{5+2\sqrt{5}}·a^2   ≈ 7.694·a^2\)

Perimeter
\(\displaystyle U= 10·a\)

Diagonal d2
\(\displaystyle d_2=\frac{1}{2} · \sqrt{10+2\sqrt{5}}·a   ≈ 1.902·a\)

Diagonal d3
\(\displaystyle d_3=\frac{1}{2} · \sqrt{14+6\sqrt{5}}·a   ≈ 2.618·a\)

Diagonal d4
\(\displaystyle d_4=\sqrt{5+2\sqrt{5}}·a   ≈ 3.078·a\)

Diagonal d5
\(\displaystyle d_5=(1+\sqrt{5})·a   ≈ 3.236·a\)

Height h
\(\displaystyle h=d_4\)

Circumcircle radius ro
\(\displaystyle r_o=\frac{1+\sqrt{5}}{2}·a   ≈ 1.618·a\)

Incircle radius ri
\(\displaystyle r_i=\frac{1}{2}·\sqrt{5+2\sqrt{5}}· a   ≈ 1.539·a\)
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