The perimeter of a square circumscribed about a circle is 16 dm. Find the perimeter of a regular

The perimeter of a square circumscribed about a circle is 16 dm. Find the perimeter of a regular hexagon inscribed in this circle.

1. Draw a regular hexagon, where AB is the side of the hexagon, O is the center of the inscribed circle, OH is the median of the triangle OO1K.

2. The sides of a regular hexagon are always equal, therefore, the diameter of a circle inscribed in a square is equal to the length of its side.

3. Find the perimeter of the square M = 16 \ 4 = 4

4. The radius of the circle R = 4 \ 2 = 2

5. Find the length of the side of a regular hexagon, using the formula

a = 2R * SIN 180 ° \ n

a = 2 * 2 * SIN 180 ° \ 5

180 \ 5 = 36

SIN 36 ° = 0.588

P = 5a = 10 * 2 * 0588 = 11.76

Answer: 11.76