Worked examples
The question
Question: find the area of a rectangle 8 long and 5 wide.
1 What area means
Area is how much space is inside.
We count the 1 by 1 squares that fit.
One row has 8 squares.
There are 5 rows.
2 Length times width
So the area is length times width: A = length × width.
Squares in a row, times the rows.
A = length × width
Now put the numbers in: length = 8 and width = 5.
A = 8 × 5
8 times 5 is 40.
So the area is 40 square units.
A = 40
3 Check
Let's check: count row by row.
5 rows of 8 squares.
8 + 8 + 8 + 8 + 8 = 40
We get 40 again.
So the area is right!
Let's look back.
First: what area means.
Then: length times width.
Last: check.
▶ Watch it solved
The question
Question: find the area of a circle with radius 3.
1 Use the rule
π is a special number for circles.
It is about 3.14.
The area of a circle is π times the radius squared: A = π × r².
So we write A = π × r².
A = π × r2
Now put the numbers in: r = 3.
A = π × 32
3² means 3 times 3.
That is 9.
32 = 3 × 3 = 9
So A = π × 9.
A = π × 9
We write it as 9π.
We keep π in the answer.
That is the exact answer.
A = 9π
2 About how much
To see about how much, put 3.14 for π.
A ≈ 9 × 3.14
9 times 3.14 is 28.26.
So the area is about 28.26 square units.
A ≈ 28.26
Let's look back.
First: use the rule.
Last: about how much.
▶ Watch it solved
The question
Question: find the area of a circle with radius 7 cm.
1 Use the rule
π is a special number for circles.
It is about 3.14.
The area of a circle is π times the radius squared: A = π × r².
So we write A = π × r².
A = π × r2
Now put the numbers in: r = 7.
A = π × 72
7² means 7 times 7.
That is 49.
72 = 7 × 7 = 49
So A = π × 49.
A = π × 49
We write it as 49π.
We keep π in the answer.
That is the exact answer.
A = 49π cm2
2 About how much
To see about how much, put 3.14 for π.
A ≈ 49 × 3.14
49 times 3.14 is 153.86.
So the area is about 153.86 cm².
A ≈ 153.86 cm2
Let's look back.
First: use the rule.
Last: about how much.
▶ Watch it solved