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Tetracontagon facts for kids

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Regular tetracontagon
Regular polygon 40.svg
A regular tetracontagon
Type Regular polygon
Edges and vertices 40
Schläfli symbol {40}, t{20}, tt{10}, ttt{5}
Coxeter diagram CDel node 1.pngCDel 4.pngCDel 0x.pngCDel node.png
CDel node 1.pngCDel 20.pngCDel node 1.png
Symmetry group Dihedral (D40), order 2×40
Internal angle (degrees) 171°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal

A tetracontagon or 40-gon is a shape with 40 sides and 40 corners.

Regular tetracontagon

All sides of a regular tetracontagon are the same length. Each corner is 171°. All corners added together equal 6840°.

Area

The amount of space a regular tetracontagon takes up is

\text{Area} = 10\left(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}+\sqrt{\left(1+\sqrt{5}+\sqrt{5+2\sqrt{5}}\right)^2+1}\right)t^2

a is the length of one of its sides.

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