Question

Sketch out various regular polygons (pentagon, hexagon, etc.) neatly on a separate sheet of pape. The perimeter of each shape must equal three inches. Record the number of sides on each shape. Then, answer the following questions:

a) How many different polygons can you make?
b) Which shape had the longest side?
c) Which shape had the shortest side?

Answer 1

You can create an infinite number of regular polygons with perimeters of three inches, each with sides equal in length. The triangle will have the longest sides, and the polygon with the most sides will have the shortest sides.

Step-by-step explanation:

To create various regular polygons with a perimeter of three inches, divide the total perimeter by the number of sides to find the side length for each shape. The number of polygons is theoretically infinite, as you can keep increasing the number of sides. For example, a triangle (with three sides) will have sides of length 1 inch each, a square (with four sides) will have sides of 0.75 inches each, and so on.

Analysis

• For a pentagon, with five sides: side length = 3 inches / 5 = 0.6 inches.
• For a hexagon, with six sides: side length = 3 inches / 6 = 0.5 inches.
• ...and this pattern would continue for other regular polygons.

Answering the student's questions:

1. The number of different polygons is limited by the precision of measurement. Technically, you could keep adding more sides indefinitely making the side length smaller each time.
2. The shape with the longest side would be the one with the fewest sides, which is a triangle in this case.
3. The shape with the shortest side would be the regular polygon with the most number of sides that you make.