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

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

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

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Dodecagons deserve to be of different types depending top top the measure up of their sides, angles, and also many such properties. Let us go through the various varieties of dodecagons.

Regular Dodecagon

A consistent dodecagon has actually all the 12 sides of equal length, all angle of same measure, and the vertices space equidistant native the center. It is a 12-sided polygon that is symmetrical. Watch the first dodecagon displayed in the figure given over which reflects a consistent dodecagon.

Irregular Dodecagon

Irregular dodecagons have sides of various shapes and also angles.There have the right to be an infinite amount of variations. Hence, they all look quite various from every other, yet they all have 12 sides. Observe the second dodecagon presented in the figure given over which shows an irregular dodecagon.

Concave Dodecagon

A concave dodecagon contends least one line segment that have the right to be drawn in between the point out on that is boundary but lies external of it. It contends least one of its interior angles higher than 180°.

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Convex Dodecagon

A dodecagon whereby no heat segment between any kind of two clues on its boundary lies exterior of that is dubbed a convex dodecagon. Nobody of its interior angles is better than 180°.

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Properties that a Dodecagon


The nature of a dodecagon are noted below i m sorry explain around its angles, triangles and also its diagonals.

Interior angles of a Dodecagon

Each inner angle the a continuous dodecagon is same to 150°. This deserve to be calculation by making use of the formula:

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

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

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

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Exterior angles of a Dodecagon

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

Diagonals of a Dodecagon

The number of distinct diagonals that have the right to be drawn in a dodecagon from all its vertices can be calculate by utilizing 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 are 54 diagonals in a dodecagon.

Triangles in a Dodecagon

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

The adhering to table recollects and also lists every the crucial properties the a dodecagon debated above.

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

Perimeter of a Dodecagon


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


Area of a Dodecagon


The formula for finding the area that a regular dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area that the dodecagon, s = the length of that side. Because that example, if the side of a continuous dodecagon procedures 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 adhering to points should be retained in mental while solving troubles related come a dodecagon.

Dodecagon is a 12-sided polygon v 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 v the formula: s × 12.

Related posts on Dodecagon

Check the end the complying with pages pertained to a dodecagon.


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

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Solution:

A polygon through 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 continual dodecagon. The neighborhood wants come buy a fencing cable to place it about the boundary of the park. If the size of one next of the park is 100 meters, calculation the size of the fencing wire forced to location all follow me the park's borders.

Solution:

Given, the size of one side of the park = 100 meters. The perimeter the the park deserve to be calculated using the formula: Perimeter of a dodecagon = s × 12, whereby s = the length of the side. Substituting the value 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 the a dodecagon is 5 units, uncover the area that the dodecagon.