Relating Area and Perimeter assignment

1. Finding perimeters of several shapes with the same area:

• You have several manipulatives in your kit that have uniform sized squares. Choose one of them.
• (A.) Take out 12 squares. Every shape you will be making for part A will have the area 12 square units, because you will make it out of 12 squares.
• Make and record (sketch) several* shapes using the 12 squares. Find the perimeter of each shape (you can make all rectangles, or you can make some shapes that are not rectangles).
• Try to make a shape with the smallest perimeter you can find. Which shape had the smallest perimeter?
• B. Repeat this process with 16 squares.
• C. What do your smallest perimeter shapes have in common?
• D. Extend: if you were going to do this with 100 squares, what kind of shape would you expect would make the perimeter would be smallest?

2. Finding areas of several shapes with the same perimeter:

• Take a piece of string with a length somewhere between 1 and 2 feet long, and knot it into a loop.
• Measure your loop of string in cm., and write down the length of the string in the loop. This will be the perimeter of all of your shapes.
• Print some cm grid paper. (You can print one at Incompetech set the spacing to 1 line per cm)
• Trace your loop of string on the grid paper in several* shapes. Find the approximate area of each shape.
• Try to find a shape that will enclose the biggest area with your loop of string. Tell what it's area is, and how you found it.

*several, for the purposes of this assignment, means at least 3.