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

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

A dodecagon is a 12-sided polygon that encloses space. Dodecagons have the right to be continuous in i beg your pardon all interior angles and also sides are equal in measure. Castle can also be irregular, with different 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 can be of different varieties depending ~ above the measure up of their sides, angles, and also many such properties. Let united state go through the various species of dodecagons.

Regular Dodecagon

A consistent dodecagon has all the 12 sides of equal length, all angle of same measure, and also the vertices space equidistant indigenous the center. It is a 12-sided polygon the is symmetrical. Watch the very first dodecagon presented in the figure given over which shows a regular dodecagon.

Irregular Dodecagon

Irregular dodecagons have sides of different shapes and also angles.There can be an infinite amount the variations. Hence, they all look quite various from each other, yet they all have 12 sides. Observe the 2nd dodecagon displayed in the figure given over which mirrors an irregular dodecagon.

Concave Dodecagon

A concave dodecagon contends least one heat segment that deserve to be drawn between the clues on that boundary but lies outside of it. It has at least one of its internal angles greater than 180°.

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Convex Dodecagon

A dodecagon whereby no heat segment between any two clues on its boundary lies outside of that is dubbed a convex dodecagon. Nobody of its internal angles is greater than 180°.

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Properties the a Dodecagon


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

Interior angles of a Dodecagon

Each inner angle the a continuous dodecagon is equal to 150°. This can be calculation by using the formula:

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

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

The amount of the internal angles that a dodecagon deserve 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 continuous dodecagon is same to 30°. If we observe the number given above, we deserve to see the the exterior angle and interior angle form a right angle. Therefore, 180° - 150° = 30°. Thus, every exterior angle has a measure of 30°. The amount of the exterior angle of a continual dodecagon is 360°.

Diagonals the a Dodecagon

The number of distinct diagonals that deserve to be drawn in a dodecagon from every its vertices can be calculate by making use of the formula: 1/2 × n × (n-3), wherein n = number 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 space 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon have the right to be damaged into a series of triangles by the diagonals which are drawn from that is vertices. The variety of triangles i m sorry are developed by these diagonals, have the right to be calculated with the formula: (n - 2), wherein n = the number of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles can be created in a dodecagon.

The complying with 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 the a Dodecagon


The perimeter of a constant dodecagon can be uncovered by detect the sum of every its sides, or, by multiply the size of one side of the dodecagon through the total number of sides. This can be stood for by the formula: p = s × 12; whereby s = size of the side. Let united state assume that the side of a regular dodecagon steps 10 units. Thus, the perimeter will 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 its side. Because that example, if the next of a constant dodecagon steps 8 units, the area of this dodecagon will 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 complying with points need to be retained in mind while solving troubles related to a dodecagon.

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

Related posts on Dodecagon

Check the end the adhering to pages regarded a dodecagon.


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

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Solution:

A polygon v 12 sides is recognized as a dodecagon. Therefore, number (a) is a dodecagon.


Example 2: There is an open up park in the form of a consistent dodecagon. The community wants to buy a fencing wire to ar it about the boundary of the park. If the size of one next of the park is 100 meters, calculate the size of the fencing wire forced to place all along the park's borders.

Solution:

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

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

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