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Area of a Regular n-Gon

A regular n-gon is a plane figure that is bounded by a chain of n straight line segments of equal length closing in a loop to form a closed polygonal chain.

The area equals one fourth of the product of the side length squared, the number of sides, and the cotangent of pi divided by the number of sides.

Formula

QuantityVariable["A", "Area"] == (Cot[Pi/QuantityVariable["n", "Unitless"]]*QuantityVariable["a", "Length"]^2*QuantityVariable["n", "Unitless"])/4

symbol description physical quantity
A area "Area"
n number of sides "Unitless"
a side length "Length"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Area of a Regular n-Gon"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Area of a Regular n-Gon"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Area of a Regular n-Gon"], {QuantityVariable["a","Length"] -> 1, QuantityVariable["A","Area"] -> 1}]
Out[3]=

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