A dodecagon is a polygon v 12 sides, 12 angles, and 12 vertices. The word dodecagon originates from the Greek word "dōdeka" which way 12 and also "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 the Dodecagons|
|3.||Properties of a Dodecagon|
|4.||Perimeter of a Dodecagon|
|5.||Area the a Dodecagon|
|6.||FAQs ~ above Dodecagon|
A dodecagon is a 12-sided polygon the encloses space. Dodecagons deserve to be consistent in i beg your pardon all interior angles and also sides are equal in measure. Castle can likewise be irregular, with different angles and sides of various measurements. The following figure shows a regular and also an rarely often, rarely dodecagon.
Dodecagons have the right to be the different species depending ~ above the measure of your sides, angles, and many together properties. Let united state go with the various types of dodecagons.
A continuous dodecagon has actually all the 12 sides of same length, all angles of equal measure, and also the vertices room equidistant indigenous the center. It is a 12-sided polygon the is symmetrical. Observe the very first dodecagon shown in the figure given above which shows a continual dodecagon.
Irregular dodecagons have sides of different shapes and also angles.There have the right to be an boundless amount that variations. Hence, they all look quite various from each other, but they all have actually 12 sides. Observe the 2nd dodecagon displayed in the number given above which shows an irregular dodecagon.
A concave dodecagon has at least one heat segment that deserve to be drawn between the clues on its boundary yet lies external of it. It has at least among its inner angles greater than 180°.
A dodecagon wherein no heat segment between any type of two points on its border lies exterior of it is called a convex dodecagon. Nobody of its internal angles is better than 180°.
Properties the a Dodecagon
The nature of a dodecagon are provided below i m sorry explain around its angles, triangles and its diagonals.
Interior angles of a DodecagonEach internal angle that a constant dodecagon is same to 150°. This deserve to be calculate by using the formula:
(frac180n–360 n), where n = the variety of sides that the polygon. In a dodecagon, n = 12. Now substituting this worth in the formula.
(eginalign frac180(12)–360 12 = 150^circ endalign)The amount of the internal angles of a dodecagon can be calculated with the help of the formula: (n - 2 ) × 180° = (12 – 2) × 180° = 1800°.
Exterior angles of a Dodecagon
Each exterior angle of a regular dodecagon is same to 30°. If we observe the figure given above, we can see that the exterior angle and interior angle type a directly angle. Therefore, 180° - 150° = 30°. Thus, each exterior angle has a measure of 30°. The amount of the exterior angle of a continuous dodecagon is 360°.
Diagonals that a Dodecagon
The variety of distinct diagonals that deserve to be drawn in a dodecagon from all its vertices can 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 space 54 diagonals in a dodecagon.
Triangles in a Dodecagon
A dodecagon have the right to be damaged into a collection of triangle by the diagonals which are attracted from that vertices. The variety of triangles which are created by these diagonals, have the right to be calculated through the formula: (n - 2), whereby n = the variety of sides. In this case, n = 12. So, 12 - 2 = 10. Therefore, 10 triangles deserve to be developed in a dodecagon.
The following table recollects and also lists every the crucial properties that a dodecagon debated above.
|Number the diagonals||54|
|Number that triangles||10|
|Sum that the interior angles||1800°|
Perimeter that a Dodecagon
The perimeter the a continual dodecagon have the right to be discovered by recognize the sum of all its sides, or, by multiply the size of one next of the dodecagon v the total variety of sides. This have the right to be stood for by the formula: p = s × 12; where s = length of the side. Let us assume the the next of a regular dodecagon actions 10 units. Thus, the perimeter will certainly be: 10 × 12 = 120 units.
Area that a Dodecagon
The formula because that finding the area of a continual dodecagon is: A = 3 × ( 2 + √3 ) × s2 , wherein A = the area the the dodecagon, s = the length of the side. Because that example, if the next 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.
The complying with points should be maintained in mind while solving problems related come a dodecagon.Dodecagon is a 12-sided polygon through 12 angles and also 12 vertices.The amount of the interior angles the a dodecagon is 1800°.The area of a dodecagon is calculated v the formula: A = 3 × ( 2 + √3 ) × s2The perimeter that a dodecagon is calculated v the formula: s × 12.
Related articles on Dodecagon
Check the end the complying with pages pertained to a dodecagon.
Example 1: Identify the dodecagon indigenous the adhering to polygons.
A polygon v 12 political parties is well-known as a dodecagon. Therefore, number (a) is a dodecagon.
Example 2: There is an open park in the shape of a continuous dodecagon. The neighborhood wants to buy a fencing cable to ar it about the boundary of the park. If the size of one next of the park is 100 meters, calculate the length of the fencing wire forced to location all follow me the park's borders.
Given, the size of one next of the park = 100 meters. The perimeter of the park deserve to be calculated making use of the formula: Perimeter that a dodecagon = s × 12, where s = the length of the side. Substituting the value 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, find the area the the dodecagon.