Sometime throughout the mid 1600s, a mathematician felt the need for a descriptive word for a 12-sided polygon. The word dodecagon originates from the Greek, dōdeka-, which way 12, and also + -gōnon, which means angled. Dodecagons deserve to be regular, an interpretation all inner angles and also sides room equal in measure. They can also be irregular, with varying angles and sides of different measurements. If friend ever try to attract a dodecagon freehand, you will certainly no doubt do an rarely often rare dodecagon.

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## Polygon

A dodecagon is a type of polygon v these properties:

It has two dimensionsIt has 12 straight sides enclosing a spaceIt has 12 internal angles

## Finding Angles and also Perimeter the a constant Dodecagon

No matter the shape, a constant polygon deserve to have that is exterior angles add to no more than 360°. Think: come go roughly the shape, you make a complete circle: 360°.

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

That was the straightforward part. The inner angles the a dodecagon room a little bit harder. You deserve to use this share formula to uncover the amount of the inner angles for an n-sided polygon (regular or irregular):

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

Once you know the sum, you have the right to divide that by 12 to acquire the measure up of each interior angle:

1800°/12 = 150°

This way each side intersects the next side just 30° much less than a straight line! That is among two reasons illustration a regular dodecagon freehand is therefore difficult. The other reason is the difficulty of drawing 12 equal-length sides.

To calculate the perimeter that a consistent dodecagon, main point one side"s measurement, s, times 12:

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

## Area that a continual Dodecagon

The easy calculations space behind us. Currently let"s tackle area the a consistent dodecagon. For a continual 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 consistent dodecagon. One next of this beautiful coin is 6.278 mm in length. What is the area that 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 seldom need that level of precision through your decimal places, for this reason feel free to round together you wish; 441.277 mm^2 is very precise.

## Working with Dodecagons

You can draw a consistent dodecagon with only a pencil, paper, compass and straightedge, yet the steps are a little bit involved.

You will certainly find few if any examples of naturally occuring dodecagons in the natural world, however coin minters choose the shape. That is really hard to counterfeit. One online coin catalog lists some 449 dodecagonal coins of plenty of different nations.

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Besides the brothers coin, Australia, Fiji and the Solomon islands mint dodecagonal coins.

## Try It!

Here is a continual dodecagon v sides measure 74 cm. What is its perimeter and also area?

Think prior to you peek!

### Perimeter:

Perimeter = 12 x sLength that 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