A dodecagon is a polygon with 12 sides, 12 angles, and also 12 vertices. The word dodecagon comes from the Greek word "dōdeka" which way 12 and also "gōnon" which method angle. This polygon deserve to be regular, irregular, concave, or convex, depending on 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 of a Dodecagon 6 FAQs top top Dodecagon

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

Dodecagons deserve to be the different types depending upon the measure up of your 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 same length, all angles of equal measure, and also the vertices space equidistant native the center. That is a 12-sided polygon that is symmetrical. Watch the very first dodecagon presented in the figure given above which mirrors a consistent dodecagon.

Irregular Dodecagon

Irregular dodecagons have actually sides of different shapes and also angles.There deserve to be an boundless amount of variations. Hence, they every look quite various from every other, however they all have 12 sides. Observe the second dodecagon displayed in the figure given over which reflects an rarely often, rarely dodecagon.

Concave Dodecagon

A concave dodecagon contends least one heat segment that deserve to be drawn in between the points on that is boundary yet lies external of it. It has at least among its internal angles higher than 180°.

Convex Dodecagon

A dodecagon where no heat segment between any type of two point out on its boundary lies outside of it is referred to as a convex dodecagon. No one of its interior angles is greater than 180°.

## Properties of a Dodecagon

The nature of a dodecagon are detailed below i beg your pardon 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 calculate by utilizing the formula:

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

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

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

Exterior angles of a Dodecagon

Each exterior edge of a regular dodecagon is equal to 30°. If us observe the number given above, we can see that the exterior angle and interior angle kind a directly angle. Therefore, 180° - 150° = 30°. Thus, every exterior angle has a measure up of 30°. The sum of the exterior angles of a regular 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 can be calculate by utilizing the formula: 1/2 × n × (n-3), whereby 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 deserve to be broken into a series of triangles by the diagonals which are attracted from that is vertices. The variety of triangles i beg your pardon are produced by these diagonals, have the right to be calculated v 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 complying with table recollects and also lists every the essential properties that a dodecagon discussed above.

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

## Perimeter that a Dodecagon

The perimeter of a continuous dodecagon have the right to be uncovered by detect the amount of every its sides, or, by multiply the length of one side of the dodecagon v the total variety of sides. This have the right to be stood for by the formula: ns = s × 12; wherein s = length of the side. Let united state assume that the side of a constant dodecagon procedures 10 units. Thus, the perimeter will be: 10 × 12 = 120 units.

## Area of a Dodecagon

The formula for finding the area that a continual dodecagon is: A = 3 × ( 2 + √3 ) × s2 , whereby A = the area that the dodecagon, s = the size of its side. Because that example, if the side of a continual dodecagon actions 8 units, the area the this dodecagon will certainly be: A = 3 × ( 2 + √3 ) × s2 . Substituting the value of that side, A = 3 × ( 2 + √3 ) × 82 . Therefore, the area = 716.554 square units.

Important Notes

The adhering to points have to be maintained in mind while solving problems related to a dodecagon.

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

## Related short articles on Dodecagon

Check the end the adhering to pages regarded a dodecagon.

Example 1: Identify the dodecagon from the following 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 continual dodecagon. The community wants to buy a fencing wire to place it about 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 ar all along the park's borders.

Solution:

Given, the size of one side of the park = 100 meters. The perimeter that the park can be calculated making use of the formula: Perimeter the a dodecagon = s × 12, where s = the length of the side. Substituting the worth 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, find the area that the dodecagon.