1. Sarah is confused about the difference between the perimeter and the area of a polygon. Explain the two concepts and the distinction be-tween them.

2. Anya wants to draw many different rectangles that have a perimeter of 16 cm. Anya draws a few rectangles, but then she stops drawing and starts looking for pairs of numbers that add to 8.

a. Why does it make sense for Anya to look for pairs of numbers that add to 8? How is she likely to use these pairs of numbers in drawing additional rectangles?

b. How could you adapt Anya's idea if you were going to draw many different rectangles that have a perimeter of 14 cm?

c. Use Anya's idea to help you draw 3 different rectangles that have a perimeter of 5 in. Label your rectangles with their lengths and widths.

3. A forest has a perimeter of 210 mi, but no in-formation is given about the shape of the forest. Justify your answers to the following (in all parts of this problem, the perimeter is still 210 mi):

a. Is it possible that the area of the forest is 3000 mi² ? Explain.

b. Is it possible that the area of the forest is 3600 mi² ? Explain.

c. If the forest is shaped like a rectangle, then is it possible that the area of the forest is 3000 mi² ? Explain.

d. If the forest is shaped like a rectangle, then is it possible that the area of the forest is 2500 mi? Explain.

4. Bob wants to find the area of an irregular shape. He cuts a piece of string to the length of the perimeter of the shape. He measures to see that the string is about 60 cm long. Bob then forms his string into a square on top of centimeter graph paper. Using the graph paper, he deter-mines that the area of his string square is about 225 cm². Bob says that the area of the irregular shape is therefore also 225 cm². Is Bob's method for determining the area of the irregular shape valid or not? Explain. If the method is not valid, what can you determine about the area of the irregular shape from the information that Bob has? Explain.