# Lesson 1

Accessing Areas and Pondering Perimeters

### 1.1: Which One Doesn’t Belong: Quadrilaterals

Which one doesn’t belong?

### 1.2: Inspect Some Rectangles

Here are some rectangles.

1. Which rectangle has the greatest perimeter?
2. Which rectangle has the greatest area?
3. Find a rectangle with the same perimeter, but an even greater area than the previous answer.
4. For the remaining questions, tables are provided to organize your work. Rectangle D has a perimeter of 32 units.
1. Find the side lengths of three different possible rectangles that have this perimeter.
2. Find a pair of side lengths for rectangle D that give the greatest area in square units.
3. 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)
5. Rectangle E has an area of 36 square units.
1. Find 3 pairs of side lengths that give this area.
2. Find a pair of side lengths for rectangle E that give the greatest perimeter in whole-number units.
3. Find a pair of side lengths for rectangle E that give the smallest perimeter in whole-number 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.

1. 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 $$x$$
2. 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
$$x$$
3. Sketch the graph of each pair of quantities, where the width is plotted along the $$x$$-axis.

1. $$x$$ and the perimeter of Rectangle A

2. $$x$$ and the area of Rectangle A

3. $$x$$ and the perimeter of Rectangle B

4. $$x$$ and the area of Rectangle B