A dodecagon is a polygon through 12 sides, 12 angles, and 12 vertices. The word dodecagon comes from the Greek native "dōdeka" which method 12 and also "gōnon" which means angle. This polygon have the right to 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 of a Dodecagon
6. FAQs on Dodecagon

A dodecagon is a 12-sided polygon the encloses space. Dodecagons have the right to be constant in which all interior angles and sides room equal in measure. Castle can likewise be irregular, with various angles and sides of different measurements. The following figure shows a regular and an rarely often rare dodecagon.

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Dodecagons can be the different species depending upon the measure of your sides, angles, and many together properties. Let united state go with the various species of dodecagons.

Regular Dodecagon

A continuous dodecagon has all the 12 political parties of equal length, all angle of same measure, and also the vertices room equidistant native the center. That is a 12-sided polygon the is symmetrical. Watch the very first dodecagon displayed in the number given over which reflects a regular dodecagon.

Irregular Dodecagon

Irregular dodecagons have sides of different shapes and angles.There deserve to be an infinite amount that variations. Hence, they all look quite different from every other, but they all have 12 sides. Watch the 2nd dodecagon presented in the figure given over which shows an rarely often rare dodecagon.

Concave Dodecagon

A concave dodecagon has at least one heat segment that deserve to be drawn in between the point out on that is boundary however lies exterior of it. It contends least among its interior angles greater than 180°.

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Convex Dodecagon

A dodecagon whereby no heat segment between any type of two clues on its border lies outside of the is referred to as a convex dodecagon. Nobody of its internal angles is better than 180°.

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Properties the a Dodecagon


The properties of a dodecagon are noted below i m sorry explain about its angles, triangles and its diagonals.

Interior angles of a Dodecagon

Each internal angle the a regular dodecagon is equal to 150°. This deserve to be calculated by utilizing the formula:

\(\frac180n–360 n\), wherein n = the variety 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 that a dodecagon can be calculated v the aid of the formula: (n - 2 ) × 180° = (12 – 2) × 180° = 1800°.

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Exterior angles of a Dodecagon

Each exterior angle of a consistent dodecagon is equal to 30°. If we observe the figure given above, we deserve to see that the exterior angle and also interior angle type a right angle. Therefore, 180° - 150° = 30°. Thus, each exterior angle has actually a measure of 30°. The amount of the exterior angles of a regular dodecagon is 360°.

Diagonals of a Dodecagon

The variety of distinct diagonals that have the right to be drawn in a dodecagon from all its vertices have the right to be calculate by using the formula: 1/2 × n × (n-3), whereby n = variety 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 deserve to be broken into a collection of triangle by the diagonals which are drawn from that is vertices. The variety of triangles i beg your pardon are developed by this diagonals, deserve to be calculated with the formula: (n - 2), wherein n = the variety of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles deserve to be developed in a dodecagon.

The complying with table recollects and lists all the necessary properties of a dodecagon debated above.

PropertiesValues
Interior angle150°
Exterior angle30°
Number the diagonals54
Number that triangles10
Sum that the interior angles1800°

Perimeter that a Dodecagon


The perimeter the a continual dodecagon can be uncovered by finding the sum of all its sides, or, by multiplying the size of one next of the dodecagon with the total variety of sides. This can be represented by the formula: ns = s × 12; whereby s = size of the side. Let us assume that the side of a continuous dodecagon procedures 10 units. Thus, the perimeter will be: 10 × 12 = 120 units.


Area of a Dodecagon


The formula because that finding the area of a consistent dodecagon is: A = 3 × ( 2 + √3 ) × s2 , whereby A = the area that the dodecagon, s = the size of that side. Because that example, if the side of a continual dodecagon actions 8 units, the area that 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 mind while solving troubles related come a dodecagon.

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

Related write-ups on Dodecagon

Check out the following pages concerned a dodecagon.


Example 1: Identify the dodecagon indigenous the adhering to polygons.

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Solution:

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


Example 2: There is an open up park in the shape of a constant dodecagon. The community wants come buy a fencing cable to location it approximately the border of the park. If the size of one side of the park is 100 meters, calculate the size of the fencing wire forced to location all along the park's borders.

Solution:

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

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

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