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

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

A dodecagon is a 12-sided polygon the encloses space. Dodecagons can be constant in which all internal angles and sides are equal in measure. Lock can additionally be irregular, with different angles and also sides of different measurements. The following number shows a regular and also an rarely often, rarely dodecagon.

Dodecagons have the right to be the different types depending ~ above the measure of their sides, angles, and many such properties. Let united state go through the various types of dodecagons.

Regular Dodecagon

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

Irregular Dodecagon

Irregular dodecagons have actually sides of different shapes and angles.There have the right to be an infinite amount of variations. Hence, they all look quite different from every other, but they all have 12 sides. Watch the second dodecagon presented in the figure given above which mirrors an rarely often, rarely dodecagon.

Concave Dodecagon

A concave dodecagon has at least one line segment that have the right to be drawn between the point out on the boundary but lies external of it. It has at least one of its internal angles greater than 180°.

Convex Dodecagon

A dodecagon wherein no heat segment between any type of two points on its boundary lies exterior of that is called a convex dodecagon. Nobody of its inner angles is higher than 180°.

## Properties that a Dodecagon

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

Interior angles of a Dodecagon

Each interior angle that a continuous dodecagon is same to 150°. This can be calculated by utilizing the formula:

(frac180n–360 n), whereby n = the variety of sides of 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 inner angles that a dodecagon have the right to be calculated v the aid of the formula: (n - 2 ) × 180° = (12 – 2) × 180° = 1800°.

Exterior angle of a Dodecagon

Each exterior edge of a constant dodecagon is equal to 30°. If us observe the number given above, we can see the the exterior angle and also interior angle kind a right angle. Therefore, 180° - 150° = 30°. Thus, each exterior angle has a measure of 30°. The amount of the exterior angle of a continual dodecagon is 360°.

Diagonals the a Dodecagon

The variety of distinct diagonals that have the right to be drawn in a dodecagon from all its vertices deserve to be calculated 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 are 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon deserve to be damaged into a collection of triangle by the diagonals i beg your pardon are drawn from the vertices. The number of triangles i m sorry are created by this diagonals, have the right to be calculated with the formula: (n - 2), whereby n = the variety of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles have the right to be formed in a dodecagon.

The adhering to table recollects and also lists every the essential properties that a dodecagon discussed above.

 Properties Values Interior angle 150° Exterior angle 30° Number that diagonals 54 Number the triangles 10 Sum the the inner angles 1800°

## Perimeter of a Dodecagon

The perimeter of a constant dodecagon can be uncovered by finding the sum of all its sides, or, by multiplying the size of one next of the dodecagon with the total variety of sides. This deserve to be represented by the formula: ns = s × 12; wherein s = length of the side. Let us assume that the side of a continuous dodecagon measures 10 units. Thus, the perimeter will be: 10 × 12 = 120 units.

## Area of a Dodecagon

The formula because that finding the area the a continuous dodecagon is: A = 3 × ( 2 + √3 ) × s2 , whereby A = the area the the dodecagon, s = the size of its side. Because that example, if the side of a continual dodecagon actions 8 units, the area that 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 following points should be preserved in mind 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 the a dodecagon is calculated with the formula: s × 12.

## Related posts on Dodecagon

Check out the complying with pages related to a dodecagon.

Example 1: Identify the dodecagon indigenous the following polygons.

Solution:

A polygon with 12 sides is recognized as a dodecagon. Therefore, figure (a) is a dodecagon.

Example 2: There is an open up park in the shape of a consistent dodecagon. The community wants to buy a fencing cable to ar it roughly the boundary of the park. If the length of one side of the park is 100 meters, calculation the length of the fencing wire forced to location all along the park's borders.

Solution:

Given, the length of one next of the park = 100 meters. The perimeter that the park deserve to be calculated using the formula: Perimeter that a dodecagon = s × 12, wherein s = the size 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, discover the area that the dodecagon.