Multiplication as Area Examples in Math

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 3×43 \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×wA = l \times w.

Answer

15 square meters

First step

1
Identify length l=5l = 5 m and width w=3w = 3 m.

Full solution

  1. 2
    Apply formula: A=l×wA = l \times w.
  2. 3
    A=5×3=15A = 5 \times 3 = 15 square meters.
  3. 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 4×74\times7 rectangle has the same area as a 7×47\times4 rectangle. Give the area.

Example 4

medium
A poster is 44 ft by 55 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 99 by 1212 rectangle filled with 33 by 33 tiles. How many tiles? What if tiles were 22 by 22?

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 33 units wide and 44 units tall. How many unit squares fit inside?

Example 4

easy
Find the area of a rectangle 55 cm by 22 cm.

Example 5

easy
A square has side 44. What is its area?

Example 6

easy
A 2×62 \times 6 rectangle holds how many unit squares?

Example 7

easy
Why does a 3×43 \times 4 rectangle hold the same number of squares as a 4×34 \times 3 rectangle?

Example 8

easy
A rectangle has area 2020 and width 44. What is its height?

Example 9

easy
A garden is 77 m by 33 m. What is its area?

Example 10

easy
How many square tiles of side 11 cover a 4×44 \times 4 floor?

Example 11

medium
An L-shaped region is made of a 4×34 \times 3 rectangle plus a 2×22 \times 2 square. What is its area?

Example 12

medium
A rectangle is 66 by 55. If you cut it in half along the length, what is the area of one half?

Example 13

medium
A floor is 88 ft by 66 ft. Tiles are 22 ft by 22 ft. How many tiles are needed?

Example 14

medium
A rectangle's area is 3636 and one side is 99. What is the perimeter?

Example 15

medium
Using the area model, compute 12×512 \times 5 by splitting 1212 into 10+210 + 2.

Example 16

medium
A poster is 33 ft by 44 ft. A second poster has double each side. What is the second poster's area?

Example 17

medium
A rug covers 2424 square feet. If it is 66 ft long, how wide is it?

Example 18

challenge
A 10×810 \times 8 rectangle has a 3×23 \times 2 hole cut out. What area remains?

Example 19

challenge
A rectangle has area 4848 and a whole-number length and width, both greater than 11. List one pair of possible side lengths where the sides differ by 22.

Example 20

challenge
Two rectangles have the same area 3636. One is 4×94 \times 9; the other is a square. What is the square's side?

Example 21

medium
Using the area model, compute 7×67 \times 6 by splitting 77 into 5+25+2.

Example 22

medium
A wall is 99 ft by 44 ft. A door 33 ft by 22 ft is not painted. What area gets painted?

Example 23

easy
A rectangle is 44 cm by 66 cm. What is its area?

Example 24

easy
A 55 by 33 rectangle contains how many unit squares?

Example 25

easy
A rectangle is 88 ft by 22 ft. How many 11-ft square tiles fill it?

Example 26

medium
A bedroom floor is 1212 ft by 1010 ft. Carpet costs $3 per square foot. What is the total cost?

Example 27

medium
A rectangle is 1515 by 44. Find its area and check using the area-model decomposition 15=10+515=10+5.

Example 28

medium
A floor is 1010 ft by 88 ft. A 44 ft by 33 ft rug sits on it. What floor area is NOT covered?

Example 29

medium
An L-shaped patio consists of a 6×46\times4 rectangle joined to a 3×23\times2 rectangle. What is the total area?

Example 30

medium
A poster is 2424 in by 3636 in. Express its area in square feet (11 ft =12=12 in).

Example 31

medium
Using the area model, compute 14×814\times8 by splitting 14=10+414=10+4.

Example 32

medium
A rectangular pool is 2020 m by 1010 m. A walking path 11 m wide is built around the entire pool. What is the area of the path?

Example 33

hard
A rectangle has area 8484 and the length is 55 more than the width. Find its dimensions.

Example 34

hard
Two rectangles have equal areas of 4848 but different perimeters. Find dimensions for the rectangle of minimum perimeter (whole-number sides).

Example 35

hard
Compute 23×1623\times16 using the area model: split 23=20+323=20+3 and 16=10+616=10+6. Show the four sub-products and the total.

Example 36

hard
A garden is 1515 ft by 2020 ft. A path of width ww is added around the inside, leaving a planting area of 176176 ft2^2. Find ww.

Example 37

hard
A rectangle has perimeter 4040 and area 9696. Find its dimensions.

Example 38

hard
Wallpaper sells in rolls of 3030 ft2^2. A wall is 1212 ft by 99 ft. How many full rolls are needed? Any waste?

Example 39

medium
A wall is 1010 ft by 88 ft with a window 33 ft by 44 ft and a door 33 ft by 77 ft cut out. What painted area remains?

Example 40

challenge
A rectangular field is enlarged so the length increases by 50%50\% and the width by 20%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≥wl\ge w).
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Background Knowledge

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

multiplicationarea