Opening subject page...
Loading your content
Learn how to cover a rectangle with square tiles and count them to find how much space it takes up!
A long, long time ago, people needed to know how big a piece of land was. Farmers wanted to know how much space they had to plant seeds. Kings wanted to know how much land they owned. So people invented a way to measure flat spaces. We call this area.
Here is a short timeline of how people learned about area:
The big question that all these people were trying to answer is: How much flat space does a shape cover? That is exactly what you will learn today using square tiles!
Before we start tiling, let's learn four important ideas. These will help everything make sense!
Let's look at a rectangle that is 5 units long and 3 units wide. Watch how we fill it with square tiles!
Look at the picture above. Each small numbered square is one unit square. The rectangle has 5 columns going across and 3 rows going down. When we count every tile, we get 15 square units. That is the area!
Notice that there are no gaps between the tiles and no tiles piling on top of each other. Every spot inside the rectangle has exactly one tile. That is what makes this a perfect tiling.
Counting tiles one by one works, but there is a faster way! You can use multiplication. Here is the special formula:
Let's use the rectangle from our picture. The length is 5 and the width is 3. So:
Why does this work? Think about it this way: if there are 5 tiles in each row, and there are 3 rows, then the total number of tiles is 5 + 5 + 5, which is the same as 5 × 3. Multiplication is just repeated addition!
The answer is always in square units. That is because we are counting squares! If each square is 1 inch on each side, we say the area is 15 square inches. If each square is 1 centimeter, we say 15 square centimeters.
Let's look at different rectangles and see how their tiles and areas change. This will help you spot the pattern!
Look at the three rectangles above. The 4 × 2 rectangle has 8 tiles. The 3 × 3 rectangle (which is a square!) has 9 tiles. The 6 × 2 rectangle has 12 tiles. Every time, the area equals the length times the width.
Here is an important thing to notice: the 3 × 3 rectangle is also a square. A square is just a special rectangle where all four sides are the same length. The formula still works!
Let's solve a problem together. Take your time and follow each step.
You now know two ways to find the area of a rectangle: counting every tile or multiplying the side lengths. Let's compare them!
| Counting Tiles | Multiplying | |
|---|---|---|
| How it works | Draw every tile and count them one by one. | Multiply the length by the width. |
| Speed | Slow for big rectangles. | Fast, even for big rectangles! |
| When it's helpful | Great for learning and checking your work. | Great once you understand why it works. |
| Can you make mistakes? | Yes — you might miscount or skip a tile. | Yes — you might multiply wrong. But you can check by counting! |
| Best for | Small rectangles and building understanding. | Any rectangle, especially big ones. |
Both ways give you the same answer! Counting tiles helps you see what area really means. Multiplying is a shortcut that saves time. Smart mathematicians learn to count first, then switch to multiplying once they feel confident.
Right now you are learning to find the area of rectangles with whole-number side lengths (numbers like 1, 2, 3, 4…). That is a fantastic start! Here is a peek at what comes later:
| What You Know Now | What You'll Learn Later |
|---|---|
| Tiling rectangles with squares to find area. | Finding area of triangles, circles, and other shapes. |
| Side lengths are whole numbers (like 3 or 5). | Side lengths can be fractions (like 2½) or decimals (like 3.5). |
| Counting tiles or multiplying two numbers. | Using special formulas for different shapes. |
| Measuring flat surfaces (area). | Measuring the space inside 3D shapes like boxes (volume). |
Everything you learn today about tiling is the foundation for those bigger ideas. When you understand that area is just counting square units, you will be ready for anything!
Now it's your turn! Try these five problems. Click "Show Answer" when you're ready to check your work.
Today you learned that area is the amount of flat space inside a shape, and we measure it in square units. To find the area of a rectangle, you can tile it — that means covering it completely with unit squares that have no gaps and no overlaps. Once you see the tiles arranged in rows and columns, you can count them all, or you can use the faster method: multiply the length times the width.
The formula Area = length × width works because multiplication is just a quick way to add equal groups. If a rectangle is 7 units long and 4 units wide, that means 4 rows of 7 tiles, which equals 28 square units. Remember: counting helps you understand, and multiplying helps you go fast. You've got both tools in your math toolbox now!