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.

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.

2. Irregular Dodecagon – It is a dodecagon with 12 sides and 12 interior angles having various measures.

Convex and Concave

1. Convex Dodecagon – It is a dodecagon where no interior angle is greater than 180°. So, no vertex points inwards.

2. Concave Dodecagon – It is a dodecagon where at least one interior angle is greater than 180°. Some of its vertices can point inwards.

Formulas

Area

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 cm^{2}

Perimeter

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 cm^{2}.

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 cm^{2} ${ =\sqrt{\dfrac{279}{3\left( 2+\sqrt{3}\right) }}}$ = 4.99 cm