Sometime during the mid 1600s, a mathematician felt the require for a descriptive word for a 12-sided polygon. Words dodecagon comes from the Greek, dōdeka-, which way 12, and + -gōnon, which way angled. Dodecagons can be regular, meaning all interior angles and sides space equal in measure. Castle can likewise be irregular, with varying angles and also sides of different measurements. If you ever shot to attract a dodecagon freehand, you will no doubt do an rarely often rare dodecagon.

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## Polygon

A dodecagon is a kind of polygon v these properties:

It has actually two dimensionsIt has actually 12 directly sides enclosing a spaceIt has actually 12 internal angles

## Finding Angles and also Perimeter of a continuous Dodecagon

No matter the shape, a constant polygon have the right to have the exterior angles include to no much more than 360°. Think: come go about the shape, you make a finish circle: 360°.

So, division 360° through the dodecagon"s twelve exterior angles. Every exterior edge is 30°.

That to be the easy part. The interior angles the a dodecagon are a little harder. You deserve to use this generic formula to discover the sum of the internal angles for an n-sided polygon (regular or irregular):

Sum of internal angles = (n-2) x 180°Sum of inner angles = 10 x 180° = 1800°

Once you recognize the sum, you can divide the by 12 to get the measure up of each internal angle:

1800°/12 = 150°

This method each side intersects the next side just 30° less than a straight line! That is one of two reasons illustration a continuous dodecagon freehand is for this reason difficult. The other reason is the challenge of illustration 12 equal-length sides.

To calculation the perimeter the a regular dodecagon, main point one side"s measurement, s, time 12:

Perimeter = 12 x sLength of one side: 17 mmPerimeter: 12 x 17 mm = 204 mm

## Area that a constant Dodecagon

The simple calculations room behind us. Currently let"s tackle area of a constant dodecagon. For a constant dodecagon with sides s, the area formula is:

A = 3 × (s)^2 × (2 + √3)

As one example, the 2017 brothers one-pound coin is a continuous dodecagon. One side of this beautiful coin is 6.278 mm in length. What is the area the this coin?

A = 3 × (s)^2 × (2 + √3)A = 3 × (6.278 mm)^2 × (2 + √3)A = 118.239852 mm^2 x 3.73205080757A = 441.277135143 mm^2A = 4.41277 cm^2

You will certainly seldom need that level the precision v your decimal places, so feel cost-free to round as you wish; 441.277 mm^2 is an extremely precise.

## Working with Dodecagons

You can draw a regular dodecagon with just a pencil, paper, compass and straightedge, yet the procedures are a bit involved.

You will certainly find few if any examples of naturally occuring dodecagons in the organic world, but coin minters favor the shape. It is an extremely hard come counterfeit. One online coin catalog lists some 449 dodecagonal coins of plenty of different nations.

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Besides the british coin, Australia, Fiji and the Solomon archipelago mint dodecagonal coins.

## Try It!

Here is a continual dodecagon with sides measuring 74 cm. What is that is perimeter and also area?

Think prior to you peek!

### Perimeter:

Perimeter = 12 x sLength of one side: 74 cmPerimeter: 12 x 74 cm = 888 cm

### Area:

A = 3 × (s)^2 × (2 + √3)A = 3 × (74 cm)^2 × (2 + √3)A = 16,428 cm^2 x 3.73205080757A = 61,310.13065192 cm^2A = 6.13101307 m^2

Decagon