Introduction to Polygon:

Polygon is a connected shape or irregular shape made up of three sides to more sides.

There are different types of polygons. Each types of polygons are based on number of sides polygon has.

Polygon has 12 sides called as Dodecagon. 12 sides polygon are also called as 12-gon. In this article, we will learn about properties of 12 sides polygon and solved problems on each properties of 12 sides polygon.

 

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Properties of 12 sides Polygon:

 

Interior angle:

Interior angle is an angle inside for the Dodecagon shape.

Let us see how to find interior angle of Dodecagon.

Formula:

Sum of interior angle of Dodecagon = ( n - 2) x 180°

Here n is number of sides.

Dodecagon has 12 number of sides.

So, sum of interior angle of Dodecagon             = ( 12 - 2 ) x 180°

                                                                     =    10  x  180°

                                                                     =  1800°

Sum of interior angles of Dodecagon is 1800 degrees.

Each interior angle of Dodecagon      = sum of interior angle of Dodecagon / number of sides

                                                           =  1800° / 12

                                                           = 150° .

Interior angle of Dodecagon is 150 degrees.

Exterior angle:

Exterior angle is an angle formed by any side of Dodecagon shape and the extension of adjacent side.

Let us see about how to calculate exterior angle of dodecagon.

Exterior angle of Dodecagon =  180° - interior angle of one side

                                               = 180° - 150°

                                               = 30°

So, exterior angle of Dodecagon is 30 degrees.

Sum of exterior angles of dodecagon = exterior angle x number of sides

                                                          =  30 ° x 12

                                                           = 360°

So, Sum of exterior angles of Dodecagon is 360 degrees.

Area:

Area of Polygon formula =   ((side)² * N)/(4Tan(π / N))

N - number of sides, side is the length of any side.

For dodecagon,

number of sides = 12 , s = 6 cm

Area of pentagon         =   ((6)2 * 12) / ( 4 Tan (3.14 / 12))

                                  =   ( 36 * 12 ) / ( 4 Tan ( 0.262 ))

                                  =    432 / ( 4 * 0.0046 )

                                  =     432 / ( 0.0184 )

                                  =     23478.3 cm2.

 

 

Other Properties of 12 sides polygon:

 

Diagonals:

The diagonal formula = `1/2` * n * (n - 3)

Let us see about how to calculate diagonals of dodecagon.

n is number of sides, n = 12.

Number of diagonals          = `1/2` * 12 * (12 - 3)

                                        = `1/2` * 12 * 9

                                        = `1/2 ` * 108

                                        = 54 .

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Triangles:

Number of triangles = n - 2.

n - number of sides

Number of triangles for dodecagon = 10 - 2

                                                   =  8 .

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