A dodecagon is a polygon with 12 sides, 12 angles, and 12 vertices. Words dodecagon comes from the Greek word "dōdeka" which means 12 and "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 of a Dodecagon
4.Perimeter that a Dodecagon
5.Area of a Dodecagon
6. FAQs top top Dodecagon

A dodecagon is a 12-sided polygon the encloses space. Dodecagons can be consistent in i m sorry all interior angles and sides room equal in measure. They can likewise be irregular, with various angles and also sides of different measurements. The following figure shows a regular and also an rarely often rare dodecagon.

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Dodecagons have the right to be of different species depending ~ above the measure of their sides, angles, and many together properties. Let us go with the various types of dodecagons.

Regular Dodecagon

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

Irregular Dodecagon

Irregular dodecagons have actually sides of various shapes and also angles.There can be an infinite amount of variations. Hence, they every look quite different from each other, but they all have actually 12 sides. Watch the second dodecagon shown in the figure given above which shows an irregular dodecagon.

Concave Dodecagon

A concave dodecagon contends least one line segment that can be drawn in between the clues on its boundary yet lies outside of it. It contends least among its internal angles higher than 180°.

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Convex Dodecagon

A dodecagon whereby no heat segment between any type of two points on its border lies outside of it is dubbed a convex dodecagon. No one of its interior angles is better than 180°.

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Properties that a Dodecagon


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

Interior angle of a Dodecagon

Each internal angle of a continual dodecagon is equal to 150°. This can be calculation by making use of the formula:

(frac180n–360 n), whereby n = the number of sides that the polygon. In a dodecagon, n = 12. Now substituting this value in the formula.

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

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

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Exterior angle of a Dodecagon

Each exterior angle of a regular dodecagon is same to 30°. If us observe the number given above, we deserve to see that 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 angle of a regular dodecagon is 360°.

Diagonals the a Dodecagon

The number of distinct diagonals that have the right to be drawn in a dodecagon from all its vertices deserve to be calculation by utilizing the formula: 1/2 × n × (n-3), wherein n = variety of sides. In this case, n = 12. Substituting the values 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 damaged into a series of triangle by the diagonals i beg your pardon are attracted from that is vertices. The variety of triangles which are created by this diagonals, can be calculated v the formula: (n - 2), whereby n = the variety of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles can be formed in a dodecagon.

The complying with table recollects and also lists all the essential properties the a dodecagon disputed above.

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

Perimeter the a Dodecagon


The perimeter of a continuous dodecagon deserve to be uncovered by detect the sum of all its sides, or, by multiplying the size of one side of the dodecagon through the total variety of sides. This deserve to be stood for by the formula: ns = s × 12; where s = length of the side. Let united state assume that the next of a regular dodecagon steps 10 units. Thus, the perimeter will be: 10 × 12 = 120 units.


Area the a Dodecagon


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

Important Notes

The following points must be kept in psychic while solving problems related come a dodecagon.

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

Related articles on Dodecagon

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


Example 1: Identify the dodecagon from the following polygons.

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Solution:

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


Example 2: There is an open up park in the shape of a regular dodecagon. The community wants come buy a fencing cable to location it around the border of the park. If the length of one next of the park is 100 meters, calculation the size of the fencing wire forced to ar all follow me the park's borders.

Solution:

Given, the size of one side of the park = 100 meters. The perimeter the the park have the right to be calculated using the formula: Perimeter the a dodecagon = s × 12, wherein s = the length of the side. Substituting the worth in the formula: 100 × 12 = 1200 meters.

Therefore, the length of the compelled 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.