Multiply Side Lengths to Find the Area of Rectangles - 3rd Grade Math

Section 1

Why Do We Need to Find Area?

Have you ever helped put tiles on a floor, or planted seeds in a garden? People have been figuring out the size of flat spaces for thousands of years! Area tells us how much space a flat shape covers. Let's look at how people learned to measure area over time.

Ancient Egypt (~3000 BCE)

Farmers along the Nile River needed to know how big their fields were. Every year the river flooded, so they measured their land again and again!

Ancient Babylon (~2000 BCE)

People in Babylon wrote math problems on clay tablets. They already knew that you could multiply two sides of a rectangle to find its area.

Ancient Greece (~300 BCE)

A math teacher named Euclid wrote a famous book about shapes. He proved why multiplying sides works for rectangles.

Today

We use area every day! Builders, painters, gardeners, and even game designers need to find the area of rectangles. Now it's your turn to learn how.

The big question is: How can we quickly find out how many square units cover a rectangle? The answer is simple — we multiply the side lengths!

Section 2

Key Ideas You Need to Know

Before we start finding area, let's make sure we understand some important words and ideas.

Area

Area is the number of square units that fit inside a flat shape. We measure area in square units like square inches or square centimeters.

Rectangle

A rectangle is a shape with 4 sides and 4 square corners. The opposite sides are always the same length.

Length & Width

The length is how long the rectangle is. The width is how wide it is. We multiply these two numbers to find the area.

Square Unit

A square unit is a tiny square (like a tile) that is 1 unit long and 1 unit wide. We count how many of these fit inside the rectangle.

✦

Key Takeaway

Think of area like covering a table with square sticky notes. You line up rows and columns of sticky notes until the whole table is covered. Instead of counting every single sticky note, you can just multiply the number in one row by the number of rows. That's exactly what finding area is!

Section 3

See It: Counting Squares vs. Multiplying

Let's look at a rectangle that is 5 units long and 3 units wide. We can fill it with little squares and then count them. Or, we can just multiply!

A rectangle 5 units wide and 3 units tall filled with 15 square units, showing that 5 × 3 = 15 square units.

Look at the picture above. The rectangle has 5 squares in each row and 3 rows. You could count every square: 1, 2, 3 … all the way to 15. But it's much faster to multiply: 5 × 3 = 15 square units. The answer is the same!

Section 4

The Area Formula

Here is the rule (we call it a formula) you can use every time you need to find the area of a rectangle.

Area of a Rectangle

Area = Length × Width

Multiply the length by the width. Your answer is in square units.

Let's make sure we understand each part:

ℹ

Length — This is how long one side of the rectangle is. For example, 7 inches. Width — This is how long the other side is. For example, 4 inches. Area — This is your answer after you multiply. In this case, 7 × 4 = 28 square inches.

Quick Example

7 × 4 = 28 square inches

A rectangle that is 7 inches long and 4 inches wide has an area of 28 square inches.

Notice that we always write "square" before the unit name. If we measure in feet, the area is in square feet. If we measure in centimeters, the area is in square centimeters. This tells everyone that we are talking about flat space inside the shape.

✦

Key Takeaway

The formula Area = Length × Width is like a magic shortcut. Instead of drawing every single little square tile and counting them one by one, you just need two numbers — the length and the width. Multiply them, and you're done!

Section 5

A Size Chart: Rectangles and Their Areas

Let's look at different rectangles and how their areas grow when the sides get bigger.

Length	Width	Multiplication	Area
2	3	2 × 3	6 square units
4	3	4 × 3	12 square units
4	5	4 × 5	20 square units
6	5	6 × 5	30 square units
8	7	8 × 7	56 square units
9	9	9 × 9	81 square units

See how the area gets bigger when the sides get bigger? When both the length and the width are big, the area grows really fast!

Section 6

Worked Example: Tiling a Garden

Let's solve a real-world problem together, step by step.

Tiling Maria's Garden

1
Problem

Maria wants to cover her garden with square tiles. Her garden is a rectangle that is 8 feet long and 6 feet wide. Each tile covers 1 square foot. How many tiles does she need?
2
Step 1 — Find the length and width

Read the problem carefully. The garden is 8 feet long and 6 feet wide. Those are our two numbers!
3
Step 2 — Write the formula

Area = Length × Width
4
Step 3 — Put in the numbers

Area = 8 × 6
5
Step 4 — Multiply!

8 × 6 = 48
6
Step 5 — Write your answer with units

The area of the garden is 48 square feet. Maria needs 48 tiles to cover her garden! 🌻

48 square feet (48 tiles)

Section 7

When Should You Use This?

Multiplying side lengths is super useful, but it only works for rectangles (and squares, since a square is a special rectangle!). Let's see when it works great and when you need something different.

Situation	Does L × W Work?	Why?
A rectangle garden	✅ Yes!	It's a rectangle — perfect for this formula.
A square rug	✅ Yes!	A square is a rectangle with all sides equal.
A book cover	✅ Yes!	Book covers are rectangles.
A triangle flag	❌ No	Triangles aren't rectangles. You'll learn a different formula later!
A circle plate	❌ No	Circles aren't rectangles. They have their own area rule.
An L-shaped room	⚠️ Sort of	Break it into two rectangles, find each area, then add!

✦

Key Takeaway

The formula Area = Length × Width is your best tool for rectangles. It's like a hammer — perfect for nails, but not for screws! For other shapes, you'll learn other tools. And for tricky shapes like an L, you can break them into rectangles, which is like using the same hammer on one nail at a time.

Section 8

What's Coming Next?

You're building skills that will help you with even bigger math ideas! Here's how what you've learned connects to what's ahead.

What You Know Now	What You'll Learn Next
Area of a rectangle = L × W	Area of triangles, parallelograms, and other shapes
Measuring in square units	Using bigger units like square meters and square miles
Whole-number side lengths	Sides that are fractions or decimals (like 3½ feet)
Flat (2D) area	Volume of 3D shapes (how much space a box takes up!)

Right now, you're working with whole numbers — that means numbers like 1, 2, 3, 4, and so on, with no fractions. As you get older, you'll use the same Area = Length × Width idea but with bigger or trickier numbers. The idea never changes — only the numbers get fancier!

Section 9

Practice Problems

Try these problems! Click "Show Answer" when you're ready to check your work.

Question 1: Problem 1 — What Does Area Mean?

Your friend says, "The area of a rectangle is 24." What does the number 24 tell us about the rectangle?

Show answer

The number 24 tells us that 24 square units fit inside the rectangle. Area means how much flat space a shape covers. Think of it like 24 little square tiles that fill up the whole rectangle with no gaps! Great job if you said something about square units fitting inside the shape.

Question 2: Problem 2 — Find the Area

A rectangle has a length of 9 inches and a width of 4 inches. What is its area?

Show answer

Use the formula: Area = Length × Width. Put in the numbers: Area = 9 × 4 = 36 square inches. Don't forget to write "square inches" — that's the unit for area when you measure in inches!

Question 3: Problem 3 — Missing Side

A rectangle has an area of 35 square feet. Its length is 7 feet. What is its width?

Show answer

We know Area = Length × Width. That means 35 = 7 × ?. Think: what number times 7 equals 35? Since 7 × 5 = 35, the width is 5 feet. Nice work! You used multiplication facts backwards — that's like doing division!

Question 4: Problem 4 — Real World: The Classroom

Mr. Lee wants to put new carpet in his classroom. The room is a rectangle that is 8 meters long and 7 meters wide. Each square meter of carpet costs $3. How much will the carpet cost in total?

Show answer

First, find the area: 8 × 7 = 56 square meters. That's how much carpet Mr. Lee needs. Next, find the cost: 56 × $3 = $168. The carpet will cost $168 in total! This problem had two steps — you found the area first, then used it to solve the money part. Awesome!

Question 5: Problem 5 — Challenge: Two Gardens

Aiden has a garden that is 6 feet long and 5 feet wide. Bella has a garden that is 10 feet long and 3 feet wide. Who has the bigger garden? Or are they the same size? Explain how you know.

Show answer

Find each area. Aiden's garden: 6 × 5 = 30 square feet. Bella's garden: 10 × 3 = 30 square feet. They are the same size! Even though the gardens look different (one is wider, one is longer), they cover the same amount of space. This shows us something really cool: rectangles can have different shapes but the same area. You're thinking like a real mathematician! 🌟

Summary

What You Learned

Summary

In this lesson, you learned that area is the amount of flat space inside a shape, measured in square units. For any rectangle, you can find the area by multiplying the length times the width. The formula is Area = Length × Width. This shortcut works because multiplying tells you how many square tiles fill up all the rows and columns inside the rectangle without counting each one.

You also learned that this formula works for real-world problems — like finding how much carpet you need or how many tiles cover a garden. Remember: always write your answer in square units (like square feet, square inches, or square centimeters). And two rectangles can look different but still have the same area if their lengths and widths multiply to the same number. You've got the tools — now go measure the world! 🎉