A dodecagon is a polygon with 12 sides, 12 angles, and also 12 vertices. Words dodecagon comes from the Greek native "dōdeka" which way 12 and "gōnon" which way angle. This polygon can be regular, irregular, concave, or convex, depending upon its properties.

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 1 What is a Dodecagon? 2 Types of Dodecagons 3 Properties the a Dodecagon 4 Perimeter of a Dodecagon 5 Area the a Dodecagon 6 FAQs top top Dodecagon

A dodecagon is a 12-sided polygon that encloses space. Dodecagons deserve to be continual in which all inner angles and also sides space equal in measure. Lock can likewise be irregular, with different angles and also sides of various measurements. The following figure shows a regular and an irregular dodecagon.

Dodecagons can be the different types depending ~ above the measure up of their sides, angles, and many together properties. Let united state go through the various species of dodecagons.

Regular Dodecagon

A continuous dodecagon has actually all the 12 sides of equal length, all angles of same measure, and also the vertices are equidistant native the center. It is a 12-sided polygon the is symmetrical. Watch the very first dodecagon presented in the number given above which mirrors a consistent dodecagon.

Irregular Dodecagon

Irregular dodecagons have sides of various shapes and angles.There deserve to be an boundless amount of variations. Hence, they every look quite various from every other, but they all have actually 12 sides. Observe the second dodecagon shown in the figure given over which reflects an irregular dodecagon.

Concave Dodecagon

A concave dodecagon has at least one heat segment that deserve to be drawn in between the points on that is boundary however lies external of it. It has at least one of its inner angles greater than 180°.

Convex Dodecagon

A dodecagon wherein no heat segment between any kind of two point out on its boundary lies exterior of it is referred to as a convex dodecagon. No one of its interior angles is higher than 180°.

## Properties of a Dodecagon

The nature of a dodecagon are provided below which explain about its angles, triangles and its diagonals.

Interior angle of a Dodecagon

Each interior angle the a constant dodecagon is equal to 150°. This deserve to be calculate by utilizing the formula:

$$\frac180n–360 n$$, whereby n = the number of sides that the polygon. In a dodecagon, n = 12. Currently substituting this value in the formula.

\beginalign \frac180(12)–360 12 = 150^\circ \endalign

The sum of the internal angles of a dodecagon deserve to be calculated through the help of the formula: (n - 2 ) × 180° = (12 – 2) × 180° = 1800°.

Exterior angle of a Dodecagon

Each exterior edge of a continuous dodecagon is same to 30°. If us observe the number given above, we can see that the exterior angle and also interior angle type a right angle. Therefore, 180° - 150° = 30°. Thus, each exterior angle has a measure up of 30°. The sum of the exterior angle of a regular dodecagon is 360°.

Diagonals of a Dodecagon

The variety of distinct diagonals that can be drawn in a dodecagon from every its vertices have the right to be calculation by utilizing the formula: 1/2 × n × (n-3), wherein n = number of sides. In this case, n = 12. Substituting the worths in the formula: 1/2 × n × (n-3) = 1/2 × 12 × (12-3) = 54

Therefore, there space 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon can be broken into a collection of triangle by the diagonals which are drawn from that vertices. The variety of triangles i m sorry are developed by this diagonals, deserve to be calculated through the formula: (n - 2), where n = the variety of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles have the right to be created in a dodecagon.

The following table recollects and also lists all the vital properties of a dodecagon disputed above.

 Properties Values Interior angle 150° Exterior angle 30° Number of diagonals 54 Number of triangles 10 Sum of the inner angles 1800°

## Perimeter the a Dodecagon

The perimeter that a consistent dodecagon can be found by recognize the amount of all its sides, or, by multiply the length of one next of the dodecagon through the total number of sides. This have the right to be stood for by the formula: p = s × 12; whereby s = size of the side. Let us assume that the next of a continual dodecagon steps 10 units. Thus, the perimeter will certainly be: 10 × 12 = 120 units.

## Area that a Dodecagon

The formula because that finding the area of a continual dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area of the dodecagon, s = the length of that is side. Because that example, if the next of a regular dodecagon measures 8 units, the area the this dodecagon will certainly be: A = 3 × ( 2 + √3 ) × s2 . Substituting the worth of its side, A = 3 × ( 2 + √3 ) × 82 . Therefore, the area = 716.554 square units.

Important Notes

The complying with points should be preserved in mental while solving troubles related come a dodecagon.

Dodecagon is a 12-sided polygon with 12 angles and also 12 vertices.The amount of the internal angles that a dodecagon is 1800°.The area of a dodecagon is calculated with the formula: A = 3 × ( 2 + √3 ) × s2The perimeter of a dodecagon is calculated through the formula: s × 12.

## Related posts on Dodecagon

Check out the adhering to pages pertained to a dodecagon.

Example 1: Identify the dodecagon from the following polygons.

Solution:

A polygon with 12 political parties is recognized as a dodecagon. Therefore, number (a) is a dodecagon.

Example 2: There is an open park in the shape of a consistent dodecagon. The community wants to buy a fencing wire to place it roughly the boundary of the park. If the length of one next of the park is 100 meters, calculate the size of the fencing wire required to ar all along the park's borders.

Solution:

Given, the size of one next of the park = 100 meters. The perimeter the the park can be calculated using the formula: Perimeter the a dodecagon = s × 12, where s = the size of the side. Substituting the value in the formula: 100 × 12 = 1200 meters.

Therefore, the length of the forced wire is 1200 meters.

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Example 3: If every side of a dodecagon is 5 units, find the area that the dodecagon.