It has 12 lines of symmetry. 6 lines of symmetry go through the opposite vertices and 6 more lines pass through the mid points of the opposite sides as shown in the diagram.
Dodecagon Lines of Symmetry
Types
Regular and Irregular
1. Regular Dodecagon – It is a dodecagon with 12 equal sides and 12 interior angles measuring 150° each. It is symmetrical.
Regular Dodecagon
2. Irregular Dodecagon – It is a dodecagon with 12 sides and 12 interior angles having various measures.
Irregular Dodecagon
Convex and Concave
1. Convex Dodecagon – It is a dodecagon where no interior angle is greater than 180°. So, no vertex points inwards.
Convex Dodecagon
2. Concave Dodecagon – It is a dodecagon where at least one interior angle is greater than 180°. Some of its vertices can point inwards.
Concave Dodecagon
Formulas
Area
Area of Dodecagon
Find the area of a dodecagon with side of 5 cm.
Solution:
As we know, Area ${\left( A\right) =3\times \left( 2+\sqrt{3}\right) \times s^{2}}$, here s = 5 cm ${\therefore A=3\times \left( 2+\sqrt{3}\right) \times 5^{2}}$ = 192.36 cm2
Perimeter
Perimeter of a Dodecagon Formula
Find the perimeter of a dodecagon with side of 6 cm.
Solution:
As we know, Perimeter (P) = 12 × s, here s = 6 cm ∴P = 12 × 6 = 72 cm
Finding the side length of a dodecagon when AREA is known
Find the side length of a dodecagon whose area is 279 cm2.
Solution:
As we know, Area ${\left( A\right) =3\times \left( 2+\sqrt{3}\right) \times s^{2}}$ ${\therefore s=\sqrt{\dfrac{A}{3\left( 2+\sqrt{3}\right) }}}$, here A = 279 cm2 ${ =\sqrt{\dfrac{279}{3\left( 2+\sqrt{3}\right) }}}$ = 4.99 cm
