A dodecagon is a polygon with 12 sides, 12 angles, and 12 vertices. The word dodecagon originates from the Greek indigenous "dōdeka" which means 12 and "gōnon" which means angle. This polygon have the right to be regular, irregular, concave, or convex, depending on its properties.

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

A dodecagon is a 12-sided polygon that encloses space. Dodecagons have the right to be continuous in which all internal angles and sides room equal in measure. They can additionally be irregular, with different angles and also sides of different measurements. The following number shows a regular and an rarely often, rarely dodecagon.

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Dodecagons deserve to be of different varieties depending top top the measure up of their sides, angles, and also many together properties. Let united state go v the various species of dodecagons.

Regular Dodecagon

A continuous dodecagon has actually all the 12 political parties of equal length, all angle of equal measure, and the vertices space equidistant native the center. It is a 12-sided polygon the is symmetrical. Watch the first dodecagon presented in the figure given above which shows a constant dodecagon.

Irregular Dodecagon

Irregular dodecagons have actually sides of different shapes and angles.There can be an unlimited amount the variations. Hence, they every look quite various from each other, however they all have actually 12 sides. Watch the second dodecagon displayed in the figure given over which shows an rarely often, rarely dodecagon.

Concave Dodecagon

A concave dodecagon has at least one heat segment that can be drawn in between the points on that boundary however lies external of it. It contends least one of its interior angles better than 180°.

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Convex Dodecagon

A dodecagon wherein no heat segment between any kind of two point out on its border lies external of it is dubbed a convex dodecagon. None of its interior angles is greater than 180°.

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Properties that a Dodecagon


The nature of a dodecagon are provided below i beg your pardon explain around its angles, triangles and also its diagonals.

Interior angle of a Dodecagon

Each internal angle of a consistent dodecagon is equal to 150°. This have the right to be calculation by using the formula:

(frac180n–360 n), where n = the variety of sides of the polygon. In a dodecagon, n = 12. Currently substituting this worth in the formula.

(eginalign frac180(12)–360 12 = 150^circ endalign)

The amount of the internal angles the a dodecagon can be calculated with the aid of the formula: (n - 2 ) × 180° = (12 – 2) × 180° = 1800°.

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Exterior angle of a Dodecagon

Each exterior edge of a constant dodecagon is equal to 30°. If we observe the figure given above, we have the right to see the the exterior angle and interior angle kind a directly angle. Therefore, 180° - 150° = 30°. Thus, every exterior angle has a measure up of 30°. The sum of the exterior angles of a constant dodecagon is 360°.

Diagonals of a Dodecagon

The variety of distinct diagonals that deserve to be attracted in a dodecagon from all its vertices can be calculation by making use of the formula: 1/2 × n × (n-3), wherein 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 room 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon deserve to be damaged into a collection of triangle by the diagonals i m sorry are attracted from its vertices. The variety of triangles i beg your pardon are developed by these diagonals, can be calculated with the formula: (n - 2), whereby n = the number of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles can be created in a dodecagon.

The following table recollects and lists all the important properties that a dodecagon discussed above.

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

Perimeter the a Dodecagon


The perimeter of a constant dodecagon have the right to be uncovered by finding the sum of every its sides, or, by multiplying the size of one side of the dodecagon with the total number of sides. This have the right to be stood for by the formula: ns = s × 12; wherein s = size of the side. Let us assume that the side of a regular dodecagon measures 10 units. Thus, the perimeter will certainly be: 10 × 12 = 120 units.


Area of a Dodecagon


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

Important Notes

The adhering to points have to be kept in mental while solving difficulties related come a dodecagon.

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

Related short articles on Dodecagon

Check out the complying with pages regarded a dodecagon.


Example 1: Identify the dodecagon indigenous the complying with polygons.

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Solution:

A polygon through 12 political parties is known as a dodecagon. Therefore, number (a) is a dodecagon.


Example 2: There is an open park in the form of a continual dodecagon. The neighborhood wants come buy a fencing wire to location it around the boundary of the park. If the size of one next of the park is 100 meters, calculate the length of the fencing wire forced 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 that a dodecagon = s × 12, where s = the length of the side. Substituting the worth in the formula: 100 × 12 = 1200 meters.

Therefore, the size of the required wire is 1200 meters.

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