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

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

A dodecagon is a 12-sided polygon the encloses space. Dodecagons have the right to be continual in i beg your pardon all interior angles and sides are equal in measure. They can additionally be irregular, with various angles and also sides of different measurements. The following number shows a regular and an rarely often, rarely dodecagon.

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

Regular Dodecagon

A constant dodecagon has all the 12 sides of same length, all angles of same measure, and the vertices space equidistant from the center. It is a 12-sided polygon the is symmetrical. Observe the first dodecagon presented in the number given over which reflects a regular dodecagon.

Irregular Dodecagon

Irregular dodecagons have actually sides of various shapes and angles.There deserve to be an infinite amount of variations. Hence, they every look quite different from each other, yet they all have 12 sides. Observe the second dodecagon presented in the figure given above which reflects an rarely often rare dodecagon.

Concave Dodecagon

A concave dodecagon contends least one line segment that can be drawn in between the points on its boundary however lies exterior of it. It has at least among its internal angles higher than 180°.

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Convex Dodecagon

A dodecagon wherein no heat segment between any two clues on its boundary lies exterior of the is dubbed a convex dodecagon. Nobody of its inner angles is higher than 180°.

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Properties of 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 the a constant dodecagon is equal to 150°. This deserve to be calculate by making use of the formula:

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

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

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

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Exterior angle of a Dodecagon

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

Diagonals the a Dodecagon

The variety of distinct diagonals that have the right to be drawn in a dodecagon from every its vertices have the right to be calculation by using the formula: 1/2 × n × (n-3), where n = number 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 space 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon deserve to be damaged into a series of triangles by the diagonals which are drawn from its vertices. The variety of triangles i beg your pardon are developed by these diagonals, have the right to be calculated with the formula: (n - 2), where n = the variety of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles can be formed in a dodecagon.

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

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

Perimeter that a Dodecagon


The perimeter of a constant dodecagon deserve to be found by finding the sum of every its sides, or, by multiply the length of one side of the dodecagon with the total number of sides. This deserve to be stood for by the formula: p = s × 12; where s = length of the side. Let united state assume the the side of a continual dodecagon actions 10 units. Thus, the perimeter will 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 , wherein A = the area the the dodecagon, s = the length of its side. For example, if the side of a continual dodecagon measures 8 units, the area of 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 difficulties related come a dodecagon.

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

Related posts on Dodecagon

Check out the adhering to pages regarded a dodecagon.


Example 1: Identify the dodecagon indigenous the adhering to 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 park in the shape of a constant dodecagon. The ar wants to buy a fencing cable 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 compelled to ar all along the park's borders.

Solution:

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

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

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