Dodecagon
Calculate the area and perimeter of a regular dodecagon from side length. Free online dodecagon calculator uses the formula A = 3(2+sqrt3)s^2 with instant results for geometry students.
About This Calculator
This dodecagon calculator computes the area and perimeter of a regular 12-sided polygon from a single side length input. A regular dodecagon has all sides equal and all interior angles measuring 150 deg. The area formula A = 3(2+sqrt3)s^2 ≈ 11.196s^2 arises from dividing the polygon into 12 congruent isosceles triangles.
The calculator uses the precise formula: Area = 3(2+sqrt3) x s^2, where s is the side length. This is derived from the general regular polygon area formula A = (n x s^2) / (4 x tan(pi/n)) with n=12. The perimeter is computed as P = 12s. Both results are displayed to two decimal places for practical use.
Geometry context: The dodecagon is related to the hexagon -- a regular dodecagon can be constructed by bisecting each side of a regular hexagon. Dodecagons are also used in the construction of the E8 lattice in mathematics and in various architectural designs throughout history.
Frequently Asked Questions
What is a dodecagon?
A dodecagon is a polygon with 12 sides and 12 angles. A regular dodecagon has all sides of equal length and all interior angles equal to 150 deg. The sum of interior angles of a dodecagon is 1800 deg (12-2 x 180 deg).
How do you calculate the area of a regular dodecagon?
The area of a regular dodecagon with side length s is A = 3(2+sqrt3)s^2 ≈ 11.196s^2. This formula comes from dividing the dodecagon into 12 isosceles triangles and summing their areas.
What is the perimeter of a dodecagon?
The perimeter of a regular dodecagon is simply 12s, where s is the side length. Since all 12 sides are equal in a regular dodecagon, the perimeter is twelve times the side length.
What are the interior and exterior angles of a dodecagon?
Each interior angle of a regular dodecagon is 150 deg. Each exterior angle (the angle between a side and the extension of an adjacent side) is 30 deg. Interior and exterior angles always sum to 180 deg.
Where are dodecagons found in real life?
Dodecagons appear in architecture (dodecagonal buildings and rooms), coins (the British threepenny coin is a dodecagon), crochet and knitting patterns, and geometry puzzles. The Australian 50-cent coin is also a regular dodecagon.
What is the relationship between a dodecagon and a circle?
A regular dodecagon can be inscribed in a circle. The circumradius (radius of the circumscribed circle) is R = s x (sqrt6 + sqrt2)/2 ≈ 1.932s. The inradius (radius of the inscribed circle) is r = s x (2+sqrt3)/2 ≈ 1.866s.