Lesson 1
Accessing Areas and Pondering Perimeters
 Let’s think about rectangles.
1.1: Which One Doesn’t Belong: Quadrilaterals
Which one doesn’t belong?
1.2: Inspect Some Rectangles
Here are some rectangles.
 Which rectangle has the greatest perimeter?
 Which rectangle has the greatest area?
 Find a rectangle with the same perimeter, but an even greater area than the previous answer.
 For the remaining questions, tables are provided to organize your work. Rectangle D has a perimeter of 32 units.
 Find the side lengths of three different possible rectangles that have this perimeter.
 Find a pair of side lengths for rectangle D that give the greatest area in square units.
 Find a pair of side lengths for rectangle D that give the smallest area in square units.
length (units) width (units) perimeter (units) area (square units)
 Rectangle E has an area of 36 square units.
 Find 3 pairs of side lengths that give this area.
 Find a pair of side lengths for rectangle E that give the greatest perimeter in wholenumber units.
 Find a pair of side lengths for rectangle E that give the smallest perimeter in wholenumber units.
length (units) width (units) perimeter (units) area (square units)
1.3: Inspect Some Tables
Here are two tables. The first shows some measurements for Rectangle A, with a side length of 5 cm. The second shows some measurements of Rectangle B, which is a square.

Complete the table for Rectangle A and be prepared to explain your reasoning.
length (cm) width (cm) perimeter (cm) area (sq cm) 5 1 5 2 5 4 5 20 5 40 5 28 5 50 5 \(x\) 
Complete the table for Rectangle B and be prepared to explain your reasoning.
length (cm) width (cm) perimeter (cm) area (sq cm) 1 1 2 2 3 3 4 16 8 100 \(x\) 
Sketch the graph of each pair of quantities, where the width is plotted along the \(x\)axis.

\(x\) and the perimeter of Rectangle A

\(x\) and the area of Rectangle A

\(x\) and the perimeter of Rectangle B

\(x\) and the area of Rectangle B
