CCSS IP Math II 6.5.1 Example 1
Show how the perimeter of a hexagon can be used to find an estimate for the circumference of a circle that has a radius of 5 meters. Compare the estimate with the circle’s perimeter found by using the formula .
- Draw a circle and inscribe a regular hexagon in the circle. Find the length of one side of the hexagon and multiply that length by 6 to find the hexagon’s perimeter.
- Create a triangle with a vertex at the center of the circle. Draw two line segments from the center of the circle to vertices that are next to each other on the hexagon.
- To find the length of , first determine the known lengths of and .
- Determine .
- Use trigonometry to find the length of .
- Determine .
- Use trigonometry to find the length of and multiply that value by 2 to find the length of .
- Find the perimeter of the hexagon.
- Compare the estimate with the calculated circumference of the circle.