A dodecagon is a polygon with 12 sides, 12 angles, and also 12 vertices. Words dodecagon comes from the Greek native "dōdeka" which method 12 and also "gōnon" which means angle. This polygon can 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 of a Dodecagon 5 Area of a Dodecagon 6 FAQs top top Dodecagon

A dodecagon is a 12-sided polygon the encloses space. Dodecagons have the right to be consistent in i beg your pardon all inner angles and sides room equal in measure. Lock can additionally be irregular, with various angles and also sides of different measurements. The following figure shows a regular and an rarely often rare dodecagon. Dodecagons have the right to be the different varieties depending upon the measure of your sides, angles, and also many together properties. Let us go v the various types of dodecagons.

Regular Dodecagon

A continual dodecagon has all the 12 sides of equal length, all angles of same measure, and the vertices are equidistant native the center. That is a 12-sided polygon the is symmetrical. Observe the very first dodecagon shown in the figure given above which mirrors a continuous dodecagon.

Irregular Dodecagon

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

Concave Dodecagon

A concave dodecagon has at least one heat segment that deserve to be drawn between the point out on the boundary however lies exterior of it. It contends least among its internal angles higher 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. None of its inner angles is higher than 180°. ## Properties of a Dodecagon

The nature of a dodecagon are listed below which explain around its angles, triangles and also its diagonals.

Interior angle of a Dodecagon

Each inner angle the a regular dodecagon is same to 150°. This can be calculation by making use of the formula:

(frac180n–360 n), wherein 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 amount of the interior angles that a dodecagon deserve to be calculated with the aid of the formula: (n - 2 ) × 180° = (12 – 2) × 180° = 1800°. Exterior angle of a Dodecagon

Each exterior angle of a consistent dodecagon is equal to 30°. If us observe the figure given above, we can see the the exterior angle and also interior angle type a straight angle. Therefore, 180° - 150° = 30°. Thus, every exterior angle has a measure up of 30°. The sum of the exterior angle of a regular dodecagon is 360°.

Diagonals of a Dodecagon

The variety of distinct diagonals that deserve to be attracted in a dodecagon from all its vertices deserve to be calculation by making use of the formula: 1/2 × n × (n-3), whereby 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 room 54 diagonals in a dodecagon.

Triangles in a Dodecagon

A dodecagon deserve to be damaged into a collection of triangles by the diagonals i beg your pardon are attracted from that is vertices. The number of triangles i beg your pardon are produced by these diagonals, can 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 complying with table recollects and lists all the important properties the a dodecagon discussed above.

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

## Perimeter that a Dodecagon

The perimeter the a continuous dodecagon can be discovered by recognize the sum of all its sides, or, by multiply the length of one side of the dodecagon with the total variety of sides. This can be stood for by the formula: ns = s × 12; where s = length of the side. Let us assume that the next 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 of a continuous dodecagon is: A = 3 × ( 2 + √3 ) × s2 , where A = the area that the dodecagon, s = the length of that side. For example, if the next of a continual dodecagon actions 8 units, the area the this dodecagon will certainly be: A = 3 × ( 2 + √3 ) × s2 . Substituting the worth of that side, A = 3 × ( 2 + √3 ) × 82 . Therefore, the area = 716.554 square units.

Important Notes

The following points should be kept in mental while solving troubles related come a dodecagon.

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

## Related articles on Dodecagon

Check the end the following pages pertained to a dodecagon.

Example 1: Identify the dodecagon from the adhering to polygons. Solution:

A polygon through 12 sides is well-known as a dodecagon. Therefore, number (a) is a dodecagon.

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

Solution:

Given, the size of one side of the park = 100 meters. The perimeter the the park have the right to be calculated utilizing the formula: Perimeter the a dodecagon = s × 12, whereby s = the size of the side. Substituting the worth 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.