Lesson 15 — Activity 2: Area of a Square
Lesson 15 — Activity 2:
Area of a Square
Getting Ready
You know that a square is a four-sided shape where all sides are equal.
In this activity, you will practise calculating the area of squares.
Courtesy of ADLC
Think about This:
Think of square shapes that you might wish to find the area of. One such shape could be tiles used on floors or walls.
Courtesy of Pixabay
Finding the Area of a Square
Looking at the image of the square above, you can see that each side has a length of 4 cm.
The
formula
for finding the area of a square is
A = s2
s is the length of one side
When you see s2, this is the same as writing:
A = s x s
To calculate the area of the square above, you would put the numbers into the formula like this:
A = s2 or A = 4 x 4
A = 16 cm2 A = 16 cm2
A = s2
s is the length of one side
If you are given the area of a square, you can find the length of the sides by taking the square root of the area.
A square root of a number is a number that when multiplied by itself will result in a given number. The square root of 4 is 2; the square root of 100 is 10.
The symbol for square root on your calculator is:
For example, if you are told that a square has an area of 25 cm2 and are asked to find the length of the side, you can do it like this:
A = s2
25 = s2
Take the square root of both sides.
The square root of s and s2 cancel each other out to leave you with just s.
Depending on which type of calculator you are using, you will either: hit the square root sign first and then put in number 25, or you will have to put in number 25 and then hit the square root sign. Try it on your calculator to see which way
works for you. Either way the answer you should get is:
5 = s
The length of one side is 5 cm.
Try This:
1. Determine the area of the square below.
Courtesy of ADLC
Area =
A = s2 or A = 47 x 47
A = 2,209 cm2
2. Determine the length of the sides of the square below.
Courtesy of ADLC
A = s2
144 cm2 = s2
12 cm = s
The length of one side is 12 cm.
Self-check!
Try This!
Try this activity to further practice working with area of squares.
What is the area of a square with sides that are 10 cm long?
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The area of this square is 100 cm2.
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The area of this square is 100 cm2.
If a square has sides that are 7 m long, how big of an area does it cover?
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The area of this square is 49 m2.
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The area of this square is 49 m2.
A square has an area of 81 km2. What is the length of each side?
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The side length of each side on this square is 9 km.
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The side length of each side on this square is 9 km.
How long is each side of a square if the total area of the square is 72 cm2? Round your answer to one decimal place.
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The side length of each side on this square is 8.5 cm.
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The side length of each side on this square is 8.5 cm.