A dodecagon is a polygon v 12 sides, 12 angles, and also 12 vertices. Words dodecagon comes from the Greek indigenous "dōdeka" which method 12 and "gōnon" which means angle. This polygon have the right to 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 that 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 deserve to be constant in i beg your pardon all internal angles and sides room equal in measure. Lock can likewise be irregular, with different angles and also sides of various measurements. The following number shows a regular and an rarely often rare dodecagon.

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

Regular Dodecagon

A consistent dodecagon has all the 12 sides of equal length, all angles of equal measure, and also the vertices are equidistant native the center. That is a 12-sided polygon that is symmetrical. Watch the an initial dodecagon shown in the figure given above which shows a continuous dodecagon.

Irregular Dodecagon

Irregular dodecagons have actually sides of different shapes and angles.There have the right to be an infinite amount the variations. Hence, they all look quite different from every other, however they all have 12 sides. Observe the 2nd dodecagon shown in the figure given over which mirrors an rarely often rare dodecagon.

Concave Dodecagon

A concave dodecagon contends least one line segment that deserve to be drawn between the points on the boundary yet lies external of it. It contends least one of its interior angles higher than 180°.

Convex Dodecagon

A dodecagon whereby no line segment between any two clues on its boundary lies external of that is called a convex dodecagon. No one of its internal angles is higher than 180°.

## Properties the a Dodecagon

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

Interior angle of a Dodecagon

Each interior angle of a consistent dodecagon is same to 150°. This can be calculate by utilizing the formula:

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

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

The sum of the inner angles the 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 angle of a continuous dodecagon is equal to 30°. If we observe the figure given above, we can see that the exterior angle and interior angle kind a right angle. Therefore, 180° - 150° = 30°. Thus, each exterior angle has actually a measure up of 30°. The amount of the exterior angle of a constant dodecagon is 360°.

Diagonals that 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 calculate by utilizing the formula: 1/2 × n × (n-3), wherein 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 are 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon can be broken into a series of triangle by the diagonals i beg your pardon are attracted from that is vertices. The number of triangles which are developed by this diagonals, can be calculated through the formula: (n - 2), where 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 adhering to table recollects and also lists every the necessary properties the a dodecagon disputed above.

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

## Perimeter the a Dodecagon

The perimeter that a constant dodecagon have the right to be discovered by detect the amount of all its sides, or, by multiply the length of one side of the dodecagon through the total number of sides. This can be stood for by the formula: p = s × 12; where s = length of the side. Let us assume that the side of a regular dodecagon steps 10 units. Thus, the perimeter will certainly be: 10 × 12 = 120 units.

## Area of a Dodecagon

The formula for finding the area the a consistent dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area the the dodecagon, s = the size of the side. For example, if the next of a continuous dodecagon measures 8 units, the area the this dodecagon will certainly be: A = 3 × ( 2 + √3 ) × s2 . Substituting the value of the side, A = 3 × ( 2 + √3 ) × 82 . Therefore, the area = 716.554 square units.

Important Notes

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

Dodecagon is a 12-sided polygon v 12 angles and also 12 vertices.The amount of the interior angles of a dodecagon is 1800°.The area that a dodecagon is calculated with 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 complying with pages pertained to a dodecagon.

Example 1: Identify the dodecagon native the complying with polygons.

Solution:

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

Example 2: There is an open up park in the form of a constant dodecagon. The neighborhood wants come buy a fencing cable to ar it around the boundary of the park. If the size of one side of the park is 100 meters, calculate the length of the fencing wire required to place all along the park's borders.

Solution:

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

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

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