A dodecagon is a polygon v 12 sides, 12 angles, and 12 vertices. Words dodecagon comes from the Greek word "dōdeka" which way 12 and also "gōnon" which way 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 the 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 have the right to be constant in i beg your pardon all inner angles and sides are equal in measure. Lock can also be irregular, with different angles and sides of different measurements. The following figure shows a regular and also an rarely often, rarely dodecagon.

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

Regular Dodecagon

A continual dodecagon has all the 12 political parties of equal length, all angle of same measure, and the vertices space equidistant native the center. The is a 12-sided polygon that is symmetrical. Observe the an initial dodecagon presented in the number given over which mirrors a continual dodecagon.

Irregular Dodecagon

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

Concave Dodecagon

A concave dodecagon has at least one line segment that can be drawn between the point out on the boundary but lies exterior of it. It contends least among its interior angles better than 180°.

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Convex Dodecagon

A dodecagon where no line segment between any type of two clues on its border lies outside of that is dubbed a convex dodecagon. Nobody of its interior angles is higher than 180°.

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Properties the a Dodecagon


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

Interior angle of a Dodecagon

Each inner angle of a constant dodecagon is equal to 150°. This have the right to be calculated by utilizing the formula:

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

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

The amount of the inner angles of a dodecagon have the right to 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 angle of a continuous dodecagon is same to 30°. If we observe the number given above, we can see that the exterior angle and interior angle type a straight angle. Therefore, 180° - 150° = 30°. Thus, every exterior angle has actually a measure up of 30°. The sum of the exterior angle of a continual dodecagon is 360°.

Diagonals of a Dodecagon

The variety of distinct diagonals that have the right to be attracted in a dodecagon from every its vertices have the right to be calculation by using the formula: 1/2 × n × (n-3), where 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 series of triangle by the diagonals i m sorry are attracted from that is vertices. The number of triangles which are produced by these diagonals, have the right to 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 deserve to be formed in a dodecagon.

The following table recollects and also lists every the vital properties that a dodecagon questioned above.

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

Perimeter of a Dodecagon


The perimeter the a consistent dodecagon can be discovered by finding the sum of all its sides, or, by multiplying the length of one side of the dodecagon with the total number of sides. This have the right to be represented by the formula: p = s × 12; whereby s = size of the side. Let us assume that the side of a continual dodecagon actions 10 units. Thus, the perimeter will certainly be: 10 × 12 = 120 units.


Area that a Dodecagon


The formula because that finding the area that a continual dodecagon is: A = 3 × ( 2 + √3 ) × s2 , wherein A = the area the the dodecagon, s = the size of that side. For example, if the next of a consistent dodecagon steps 8 units, the area that this dodecagon will be: A = 3 × ( 2 + √3 ) × s2 . Substituting the worth of that side, A = 3 × ( 2 + √3 ) × 82 . Therefore, the area = 716.554 square units.

Important Notes

The complying with points need to be maintained in mental while solving problems related to a dodecagon.

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

Related articles on Dodecagon

Check out 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 sides is well-known as a dodecagon. Therefore, number (a) is a dodecagon.


Example 2: There is an open park in the form of a continuous dodecagon. The neighborhood wants come buy a fencing wire to ar it roughly the boundary of the park. If the size of one side of the park is 100 meters, calculate the size of the fencing wire compelled to place all follow me the park's borders.

Solution:

Given, the size of one next of the park = 100 meters. The perimeter that the park deserve to be calculated utilizing 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 size of the required wire is 1200 meters.

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