Learn About Area
How much space does this board take up? 🤔
👉 To figure that out, let's find the board's area!
What is Area?
Area is the amount of space a flat shape or surface takes up.
Tip: Only two-dimensional objects have an area. Three-dimensional objects have volume.
The cover of a book is flat. The front of a closet door is flat.
How do you find the area of something?
Let's find the area of a grid like this board
One way to find the area of a grid is to count all the squares in it.
Let's count them now.
How many squares are there?
That's right! There are 30 squares.
😀 The area of the board is 30 square units.
1 square is 1 square unit.
But counting is pretty slow. Let's learn a faster way.
Using Multiplication to Find the Area
To find the area of a grid like a rectangle or a square, just multiply the height times the width.
Height x Width = Area
Why does this work? 🤔
Because grids are just columns multiplied by some number of rows! 🤓
How many rows and columns does our grid have?
Now what happens when we multiply the number of rows (5) times the columns (6)?
5 x 6 = 30
We get the same answer from multiplying as we do from adding all of the squares!
Multiply the length and width of any rectangle or square to get its area quickly.
Units of Area
Just like length, weight and time, area also has some units of measurement.
Units of area tell us how big or small an area actually is.
Imagine that this is the measurement of each square on the board.
We see that the square is 1 centimeter (cm) long. This is its length.
The square is also 1 centimeter (cm) wide. This is its width.
👉The area of a square 1 cm wide, and 1 cm tall is 1 square centimeter.
Square centimeter is a unit of measurement for area. It's written as cm².
In the United States, people also use square inches as a unit of measurement! It's written as sq.in. or in².
👉The area of a square 1 in wide, and 1 in tall is 1 square inch.
So, what's the area of our board?
We know that it's 30 square units.
If the area of each square is 1 cm² , then the area of the board is 30 cm².👍
Area of Larger Spaces
What if we want to measure the area of larger spaces, like this field of grass?
What unit of measurement should we use? 🤔
😌 Square centimeter would be too small.
For larger spaces, the unit of measurement often used is square meter. It's written as m².
When our unit of area is the square meter, it means that the area of each square is 1 m². 👍
In other words, the length of each square unit is 1 meter and its width is also 1 meter. 👍
Now, let's measure the area of the yard.
👉 A grid can help us count the square units.
Each square unit has an area of 1 m².
How many square units cover the inside of the yard?
You can figure out by counting the squares, but that would take a long time.
Let's multiply the columns by the rows instead.
5 x 9 = ?
What do we get? 45 square units!
So, the area of the yard is 45 m². 🎉
In the United States, people often use square feet instead of square meters!
1 square foot is the area of a 1 ft by 1 ft square. It's abbreviated as sq. ft. or ft².
Square feet are smaller than square meters.
1 m2 can fit over 10 ft².
Estimating the Area of Irregular Surfaces
It's easy to find the area of a grid. We just count the squares inside, or multiply the length times the width.
🤔 But what if you want to estimate the area of an irregular surface, like this red eraser?
👉 First, count all the full squares inside the eraser.
There's only one - the blue square. It's area is 1 m².
👉 For the other squares use this estimation rule:
- If the eraser covers more than half of it, count it as 1 m².
- If the eraser covers less than half the grid, count it as 0.
Look at squares 1, 3, 4, and 6:
Each of these squares covers more than half of one square. So, their total area is 4 m².
Look at squares 2, 5, and 7:
Each of them cover less than half a square. So, their total area is 0.
👉 We bring the three totals together.
1 + 4 + 0 = 5 square meters
The estimated area of the eraser is 5 m².
Great work! 🎉
Watch and Learn
Now, you can try the practice exercises. 💪