A regular 12-gon is inscribed inside a circle.

Question

   A regular 12 gon. The lengths b and h as described in the problem are marked. 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?

 

 

 

The area of the circle is equal to 6bh

 The area of the circle is slightly greater than 6bh.

 The area of the circle is equal to πh2.

 The area of the circle is slightly less than 6bh.

Answer 1

The area of each triangle is ½bh, so the area of the 12-gon is 12×½bh=6bh. The area of the circle is slightly more than this, 2nd answer.