Calculate Square Side Length: Finding Dimensions When Area = 81

Q: What's the difference between area and perimeter of a square?

Area is the space inside the square ($ L^2 $), while perimeter is the distance around the outside ($ 4L $). Don't mix them up!

Q: How do I find the square root of 81?

Think: what number times itself equals 81? You can count by perfect squares: $ 1^2 = 1, 2^2 = 4, 3^2 = 9... 9^2 = 81 $. So $ \sqrt{81} = 9 $!

Q: Why do we only use the positive square root?

Side lengths represent distance, which is always positive! Even though $ (-9)^2 = 81 $ too, we can't have negative length in geometry.

Q: How can I check if my answer is right?

Square your answer! If you got 9 for the side length, check: $ 9^2 = 9 \times 9 = 81 $. This matches the given area, so you're correct!

Square Area with Perfect Square Roots

A square has an area of 81.

How long are its sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the side of the square

00:03 Use the formula for calculating the area of a square (side squared)

00:08 Substitute appropriate values and solve for the side

00:15 Extract the root

00:21 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A square has an area of 81.

How long are its sides?

Step-by-step solution

Remember that the area of a square is equal to the side of the square raised to the second power.

Formula for the area of the square:

$A=L^2$

We calculate the area of the square:

$81=L^2$

We calculate the root:

$\sqrt{81}=a$

$9=a$

Final Answer

$9$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared: $A = L^2$
Technique: Find square root of area: $\sqrt{81} = 9$
Check: Verify by squaring your answer: $9^2 = 81$ ✓

Common Mistakes

Avoid these frequent errors

Dividing area by 4 instead of taking square root
Don't divide 81 by 4 to get 20.25! This confuses area formula with perimeter. The area formula is $A = L^2$ , so you need the square root. Always take $\sqrt{\text{area}}$ to find side length.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square equivalent to?

FAQ

Everything you need to know about this question

What's the difference between area and perimeter of a square?

Area is the space inside the square ( $L^2$ ), while perimeter is the distance around the outside ( $4L$ ). Don't mix them up!

How do I find the square root of 81?

Think: what number times itself equals 81? You can count by perfect squares: $1^2 = 1, 2^2 = 4, 3^2 = 9... 9^2 = 81$ . So $\sqrt{81} = 9$ !

What if the area isn't a perfect square?

You'll get a decimal or need to leave your answer as a square root. For example, if area = 50, then side length = $\sqrt{50} \approx 7.07$ .

Why do we only use the positive square root?

Side lengths represent distance, which is always positive! Even though $(-9)^2 = 81$ too, we can't have negative length in geometry.

How can I check if my answer is right?

Square your answer! If you got 9 for the side length, check: $9^2 = 9 \times 9 = 81$ . This matches the given area, so you're correct!

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