SOLUTION: Please help me solve this question! A regular 12-gon is inscribed inside a circle. The 12 congruent triangles that make up the 12-gon each have a base of length b and heigh

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me solve this question! A regular 12-gon is inscribed inside a circle. The 12 congruent triangles that make up the 12-gon each have a base of length b and heigh      Log On


   



Question 1143309: Please help me solve this question!
A regular 12-gon is inscribed inside a circle.
The 12 congruent triangles that make up the 12-gon each have a base of length b and height of length h. Which of the following statements is true?
(A) The area of the circle is slightly less than 6bh
(B) The area of the circle is equal to πh^2
(C) The area of the circle is equal to 6bh
(D) The area of the circle is slightly greater than 6bh
I personally believe that the answer is D, because I know that since the circle contains the 12-gon, the circle's area has to be slightly larger but I just want to make sure this is correct!

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Your reasoning is correct....

The area of the 12-gon is the area of the 12 congruent triangles:

%2812%29%28%281%2F2%29%28bh%29%29+=+6bh

The 12-gon is inscribed in the circle, so the area of the circle is greater than that....