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Pentadecagon facts for kids

Kids Encyclopedia Facts
Regular pentadecagon
Pentadecagon.svg
A regular pentadecagon
Type Regular polygon
Edges and vertices 15
Schläfli symbol {15}
Coxeter diagram CDel node 1.pngCDel 15.pngCDel node.png
Symmetry group Dihedral (D15), order 2×15
Internal angle (degrees) 156°
Dual polygon Self
Properties Convex, cyclic, equilateral, isogonal, isotoxal

A pentadecagon or quindecagon or 15-gon is a shape with 15 sides and 15 corners.

Regular pentadecagon

All sides of a regular pentadecagon are the same length. Each corner is 147.27°. All corners added together equal 156°.

Area

The amount of space a regular pentadecagon takes up is


 \begin{align} A = \frac{15}{4}a^2 \cot \frac{\pi}{15} & = \frac{15}{4}\sqrt{7+2\sqrt{5}+2\sqrt{15+6\sqrt{5}}}a^2 \\
                 & = \frac{15a^2}{8} \left( \sqrt{3}+\sqrt{15}+
                                            \sqrt{2}\sqrt{5+\sqrt{5}} 
                                     \right) \\
                 & \simeq 17.6424\,a^2.
 \end{align}

a is the length of one of its sides.

Uses

3.10.15 vertex.png
A regular triangle, decagon, and pentadecagon can completely fill a plane vertex.

Images for kids

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