Find the area of the regular dodecagon inscribed in a circle if one vertex is at (3, 0).

Area of the regular dodecagon inscribed in a circle will be 27 square units.

Step-by-step explanation:

A regular dodecagon is the structure has twelve sides and 12 isosceles triangles inscribed in a circle as shown in the figure attached.

Since angle formed at the center by a polygon =

Therefore, angle at the center of a dodecagon = = 30°

Since one of it's vertex is (3, 0) therefore, one side of the triangle formed or radius of the circle = 3 units

Now area of a small triangle =

where a and b are the sides of the triangle and θ is the angle between them.

Now area of the small triangle =

=

Area of dodecagon = 12×area of the small triangle

= 12×

= 27 unit²

Therefore, area of the regular octagon is 27 square unit.

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

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