Lesson 8.1 · Area
Understanding area
How much paper do you need to cover a book? How many tiles fit on a floor? These questions are about area: how much flat space a shape covers.
Covering a shape with squares
To measure length, you line up units end to end. To measure area, you cover a shape with small squares.
A unit square is a square whose sides are each 1 unit long. We say it has an area of 1 square unit.
Here is a shape covered with unit squares. Each 🟦 is 1 square unit.
🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦
Count the squares: there are 10. The area of this shape is 10 square units.
Definition
Area
Area is the amount of flat space a shape covers. You find it by counting how many unit squares cover the shape with no gaps and no overlaps.
No gaps, no overlaps
The squares must fit together like floor tiles.
- A gap is a space with no square in it. Gaps make your count too small.
- An overlap is where two squares sit on top of each other. Overlaps make your count too big.
When the squares touch edge to edge, with no gaps and no overlaps, your count is the true area.
Units of area
Squares come in different sizes. The name of the unit tells you the size of the square.
| Unit | The square has sides of... | Good for measuring... |
|---|---|---|
| square centimeter (sq cm) | 1 centimeter | a stamp or a sticker |
| square inch (sq in) | 1 inch | a photo or a notebook |
| square meter (sq m) | 1 meter | a classroom floor |
| square foot (sq ft) | 1 foot | a rug or a bedroom |
Always write the unit with your answer. "12" is not an area. "12 square inches" is.
Area is counted in square units
Count the unit squares that cover the shape. The area is that number of square units, such as square centimeters or square feet.
Shapes that are not rectangles
You can count the area of any shape made of squares, not just rectangles.
Worked example: Count the squares
Each 🟦 is 1 square unit. What is the area?
🟦🟦🟦🟦
🟦🟦🟦🟦
🟦🟦🟦🟦
Count row by row: 4, 8, 12. The area is 12 square units.
Worked example: An L shape
Each 🟦 is 1 square centimeter. What is the area of this shape?
🟦🟦🟦🟦🟦
🟦🟦
🟦🟦
The top row has 5 squares. The next two rows have 2 each.
The area is 9 square centimeters.
Worked example: Which covers more?
Shape A:
🟦🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦🟦
Shape B:
🟦🟦🟦🟦
🟦🟦🟦🟦
🟦🟦🟦🟦
Both use the same size squares. Which shape has the greater area?
Shape A has 2 rows of 6, so it has 12 squares. Shape B has 3 rows of 4, so it also has 12 squares. They have the same area, even though they look different.
Common mistake
Don't count the squares along the edge only. Area counts every square inside the shape, including the ones in the middle.
Tip
Count row by row. If every row has the same number of squares, you can skip count or multiply. You will learn more about this in the next lesson.
Practice
Each 🟦 is 1 square unit. What is the area, in square units?
🟦🟦🟦🟦
🟦🟦🟦🟦
Type a number.
Which unit would you use to measure area?
Each 🟦 is 1 square unit. What is the area, in square units?
🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦
🟦🟦🟦🟦🟦
Type a number.
Each 🟦 is 1 square centimeter. What is the area of this shape, in square centimeters?
🟦🟦🟦🟦
🟦🟦🟦🟦
🟦🟦
Type a number.
Kim covers a card with sticky notes to find its area. Some of her notes lie on top of each other. What will happen to her count?
Shape A is 3 rows of 3 unit squares. Shape B is 2 rows of 4 unit squares. Which has the greater area?
Leo builds a shape with 14 unit squares. Then he takes 3 squares away. What is the area of his new shape, in square units?
Type a number.
Each 🟦 is 1 square inch. What is the area of this shape, in square inches?
🟦🟦🟦
🟦
🟦🟦🟦
Type a number.