Calculate Side Length of a Square with Area = 1: Basic Geometry Problem

Q: Why is the answer 1 and not 0.5 or 2?

Since area = side², we need a number that when squared equals 1. Only $ 1^2 = 1 $ works! If side = 0.5, then area = 0.25. If side = 2, then area = 4.

Q: How do I remember the area formula for squares?

Think of it as "side times side" or s × s = s². A square with side 3 has area 3 × 3 = 9. It's always the side length multiplied by itself!

Q: What if the area was a different number like 4 or 9?

Same process! Take the square root of the area. For area = 4, side = $ \sqrt{4} = 2 $. For area = 9, side = $ \sqrt{9} = 3 $.

Q: Can a square have a fractional side length?

Absolutely! If area = $ \frac{1}{4} $, then side = $ \sqrt{\frac{1}{4}} = \frac{1}{2} $. Always check: $ (\frac{1}{2})^2 = \frac{1}{4} $ ✓

Q: Do I always need to take the square root to find side length?

Yes, when you know the area! The square root "undoes" the squaring in the area formula. It's the reverse operation that gets you back to the original side length.

Square Area with Unit Measurements

A square has an area of 1.

How long are its sides?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the length of a square's side.

00:07 Use the area formula: side times side equals area.

00:13 Now, plug in the area value, and solve for the side length.

00:18 To find the side, take the square root of the area.

00:26 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A square has an area of 1.

How long are its sides?

Step-by-step solution

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Now, we replace the data in the formula:

$1=L^2$

We extract the root:

$\sqrt{1}=L$

$L=1$

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared (A = s²)
Technique: Take square root of area: $\sqrt{1} = 1$
Check: Verify by squaring answer: $1^2 = 1$ matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing area formula with perimeter
Don't think area = 4 × side length = wrong answer of 0.25! That's the perimeter formula divided by 4. The area formula uses squaring, not multiplication by 4. Always remember area = side²

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

Why is the answer 1 and not 0.5 or 2?

Since area = side², we need a number that when squared equals 1. Only $1^2 = 1$ works! If side = 0.5, then area = 0.25. If side = 2, then area = 4.

How do I remember the area formula for squares?

Think of it as "side times side" or s × s = s². A square with side 3 has area 3 × 3 = 9. It's always the side length multiplied by itself!

What if the area was a different number like 4 or 9?

Same process! Take the square root of the area. For area = 4, side = $\sqrt{4} = 2$ . For area = 9, side = $\sqrt{9} = 3$ .

Can a square have a fractional side length?

Absolutely! If area = $\frac{1}{4}$ , then side = $\sqrt{\frac{1}{4}} = \frac{1}{2}$ . Always check: $(\frac{1}{2})^2 = \frac{1}{4}$ ✓

Do I always need to take the square root to find side length?

Yes, when you know the area! The square root "undoes" the squaring in the area formula. It's the reverse operation that gets you back to the original side length.

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