Student Name

Date

The Problem

If you have 48 inches of wood that you will use to build a picture frame. What is the largest size picture that you can frame. What shape will it have?

Perimeter and Area

• Perimeter is the distance around the outside of a shape, figure, or object

• The perimeter is found by adding the length of all of the sides

• Area is the square units that will fit inside a shape or figure

• The area is found by multiplying the length and width of the figure

The Solution

• Because I have 48 inches of wood, 48 inches is the largest perimeter of a frame that can be built.

1. First, I listed all of the possible combinations of length and width for a picture frame that would add up to a total perimeter of 48 inches.

2. Next, I multiplied all of the different combinations to determine the greatest area.

3. The greatest area was when the length and width were 12 inches each creating an area of 144 square inches.

What happens when you change the length and width of a shape without changing the

perimeter? • Click on the link below to explore the answer!

The Reasoning

The Conclusion• The most

abundant area is produced by the “special” rectangle known as a

SQUARE!