Can you help me solve this geometry word problem?

It says, "Mrs. Frank loves the clock in the classroom because it has the school colors, green and purple. The shape pf the clock is a regular dodecagon with a radius of 14 centimeters. Centered on the clock's face is a green circle of radius 9 centimeters. If the region outside the circle is purple, which color has more area?"

I know the area of the green is 81 pi which is about 254.5cm squared, and that the area of the purple is 588 - 81 pi which is about 333.5cm squared, so the area of purple is greater. I'm just not sure how to get the work. Can anyone show the work and explain how I could get the answer? Please and thank you xx

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  • 6 years ago
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    Area of the dodecagon: did you make a diagram ?

    you can make 12 isosceles triangles whose legs are 14 cm (made of radii) and whose central angle is 30º

    the area of one of these triangles is: (1/2)(14)(14)(sin 30) = 49 cm^2

    [area of a triangle = (1/2) ab sin C ]

    there are 12 of these triangles: 12 * 49 = 588 cm^2

    qed

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