Multiplication as Area Examples: 46 Problems with Answers

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multiplication as Area.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Understanding multiplication as calculating the area of a rectangle: length times width gives the number of unit squares that fit inside. This visual model connects arithmetic to geometry.

A $3 \times 4$ rectangle has 12 unit squares inside—multiplication counts them.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Area sees multiplication as counting the unit squares that tile a rectangle: length times width.

Common stuck point: The procedure for multiplication as area is the easy part; the trap is adding length and width instead of multiplying. Asking "Am I counting the unit squares that fill a rectangle of given length and width?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I counting the unit squares that fill a rectangle of given length and width?

Worked Examples

Example 1

easy

A rectangular garden is 5 meters long and 3 meters wide. What is its area? Use

A = l \times w

Answer

15 square meters

First step

Identify length

l = 5

m and width

w = 3

Full solution

2
Apply formula: $A = l \times w$ .
3
$A = 5 \times 3 = 15$ square meters.
4
The garden's area is 15 m².

Area of a rectangle = length × width. Think of tiling the garden with 1m × 1m squares: 5 columns × 3 rows = 15 squares.

Example 2

medium

A tile floor is 8 feet long and 6 feet wide. Each tile is 1 square foot. How many tiles are needed to cover the floor?

Example 3

easy

Explain why a

4\times7

rectangle has the same area as a

7\times4

rectangle. Give the area.

Example 4

medium

A poster is

4

ft by

5

ft. The same poster is enlarged so each side doubles. How many times bigger is the new area?

Example 5

hard

A floor mosaic shows a

9

12

rectangle filled with

3

3

tiles. How many tiles? What if tiles were

2

2

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy

A rectangle has length 7 cm and width 4 cm. Find its area.

Example 2

medium

A wall has an area of 54 square feet. It is 9 feet tall. How wide is the wall?

Example 3

easy

A rectangle is

3

units wide and

4

units tall. How many unit squares fit inside?

Example 4

easy

Find the area of a rectangle

5

cm by

2

cm.

Example 5

easy

A square has side

4

. What is its area?

Example 6

easy

2 \times 6

rectangle holds how many unit squares?

Example 7

easy

Why does a

3 \times 4

rectangle hold the same number of squares as a

4 \times 3

rectangle?

Example 8

easy

A rectangle has area

20

and width

4

. What is its height?

Example 9

easy

A garden is

7

m by

3

m. What is its area?

Example 10

easy

How many square tiles of side

1

cover a

4 \times 4

floor?

Example 11

medium

An L-shaped region is made of a

4 \times 3

rectangle plus a

2 \times 2

square. What is its area?

Example 12

medium

A rectangle is

6

5

. If you cut it in half along the length, what is the area of one half?

Example 13

medium

A floor is

8

ft by

6

ft. Tiles are

2

ft by

2

ft. How many tiles are needed?

Example 14

medium

A rectangle's area is

36

and one side is

9

. What is the perimeter?

Example 15

medium

Using the area model, compute

12 \times 5

by splitting

12

into

10 + 2

Example 16

medium

A poster is

3

ft by

4

ft. A second poster has double each side. What is the second poster's area?

Example 17

medium

A rug covers

24

square feet. If it is

6

ft long, how wide is it?

Example 18

challenge

10 \times 8

rectangle has a

3 \times 2

hole cut out. What area remains?

Example 19

challenge

A rectangle has area

48

and a whole-number length and width, both greater than

1

. List one pair of possible side lengths where the sides differ by

2

Example 20

challenge

Two rectangles have the same area

36

. One is

4 \times 9

; the other is a square. What is the square's side?

Example 21

medium

Using the area model, compute

7 \times 6

by splitting

7

into

5+2

Example 22

medium

A wall is

9

ft by

4

ft. A door

3

ft by

2

ft is not painted. What area gets painted?

Example 23

easy

A rectangle is

4

cm by

6

cm. What is its area?

Example 24

easy

5

3

rectangle contains how many unit squares?

Example 25

easy

A rectangle is

8

ft by

2

ft. How many

1

-ft square tiles fill it?

Example 26

medium

A bedroom floor is

12

ft by

10

ft. Carpet costs $3 per square foot. What is the total cost?

Example 27

medium

A rectangle is

15

4

. Find its area and check using the area-model decomposition

15=10+5

Example 28

medium

A floor is

10

ft by

8

ft. A

4

ft by

3

ft rug sits on it. What floor area is NOT covered?

Example 29

medium

An L-shaped patio consists of a

6\times4

rectangle joined to a

3\times2

rectangle. What is the total area?

Example 30

medium

A poster is

24

in by

36

in. Express its area in square feet (

1

=12

in).

Example 31

medium

Using the area model, compute

14\times8

by splitting

14=10+4

Example 32

medium

A rectangular pool is

20

m by

10

m. A walking path

1

m wide is built around the entire pool. What is the area of the path?

Example 33

hard

A rectangle has area

84

and the length is

5

more than the width. Find its dimensions.

Example 34

hard

Two rectangles have equal areas of

48

but different perimeters. Find dimensions for the rectangle of minimum perimeter (whole-number sides).

Example 35

hard

Compute

23\times16

using the area model: split

23=20+3

and

16=10+6

. Show the four sub-products and the total.

Example 36

hard

A garden is

15

ft by

20

ft. A path of width

w

is added around the inside, leaving a planting area of

176

^2

. Find

w

Example 37

hard

A rectangle has perimeter

40

and area

96

. Find its dimensions.

Example 38

hard

Wallpaper sells in rolls of

30

^2

. A wall is

12

ft by

9

ft. How many full rolls are needed? Any waste?

Example 39

medium

A wall is

10

ft by

8

ft with a window

3

ft by

4

ft and a door

3

ft by

7

ft cut out. What painted area remains?

Example 40

challenge

A rectangular field is enlarged so the length increases by

50\%

and the width by

20\%

. By what percent does the area increase?

Example 41

challenge

A rectangle has integer side lengths. Its area equals its perimeter. Find all such rectangles (with

l\ge w

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Related Concepts

Multiplication Area Area Distributive Property

Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplicationarea