Can other rectangles have the same area as this one?

In this lesson you will learn that rectangles can have the

same area but different perimeter by building

rectangles and organizing the information into a chart.

Let’s Review

Perimeter tells us the distance that goes around the polygon.

Perimeter

Let’s Review

Length

Width

A Common Mistake

Perimeter

Area

Mixing up area and perimeter.

Core Lesson

Area = 9 square units

Area = 9 square units

Core Lesson

Perimeter = 20 units

Perimeter = 12 units

Core Lesson

Rectangle #1 Rectangle #2

Rectangle #3

Rectangle Perimeter Length Width Area

#1

#2

#3

12 square units

12 square units

2 units

12 square units

4 units

1 unit

6 units

3 units

12 units

16 units

14 units

26 units

Core Lesson

Rectangle #1

Rectangle #2

Rectangle #3

Core Lesson

Rectangle Perimeter Length Width Area#1

#2

#3

16 square units8 units 2 units20 units

16 units 4 units 4 units 16 square units

34 units 1 units 16 units 16 square units

In this lesson, you have learned that rectangles can

have the same area but different perimeter by building rectangles and organizing the

information into a chart.

Guided Practice

Can rectangles with a different perimeter have the same area as this rectangle?

Guided Practice

Rectangle #1Rectangle #2

Perimeter Length Width Area

4 square units2 units 2 units8 units

10 units 4 units 1 units 4 square units

#1

#2

Rectangle

Extension Activities

Sally asked her father to build a fence around her backyard. Sally wanted the backyard to be 36 square feet. In order to have the biggest backyard, Sally’s father would need to buy more fencing. Create a chart to show how many polygons Sally’s backyard could be with 36 square feet. Then circle the rectangle that would be the biggest (which one has the biggest perimeter)

Extension Activities

This rectangle has an area of 8 square units. Fill in the chart to show the possible perimeters.

Area Length Width Perimeter

8 square units

8 square units

Extension Activities

Fill in this chart. You can use square tiles to help you visualize the rectangles.

Perimeter Length Width Area

20 units 7 units 21 square units

20 units 1 unit

20 units 20 square units

20 units 6 units

20 units 8 units

Quick Quiz

Here are some rectangles with an area of 24 square units. Circle the rectangles with a perimeter greater than 24 units.

Quick Quiz

Which rectangle has a larger perimeter? How much larger is that perimeter?

Rectangle #1Rectangle #2