Square Area Formula: Determining the Expression for ABCD Square

Q: How do I know which expression represents the side length?

Look at the diagram carefully! The side is labeled as x/y, so you need to square this entire expression to get the area.

Q: Why isn't the area just x² or y²?

Because the side length isn't just x or y - it's the fraction x/y. When you square a fraction, you square both the numerator and denominator: $ \left(\frac{x}{y}\right)^2 = \frac{x^2}{y^2} $

Square Area Formulas with Algebraic Expressions

Look the square below:

Which expression represents its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the area of the square.

00:07 We can determine the side length using the given data.

00:12 Remember, the area of a square is found using the formula: side, t imes side.

00:19 We'll substitute the correct values and calculate the area toge ther.

00:29 Be sure to square both the numerator and the denominator.

00:34 Great job! And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look the square below:

Which expression represents its area?

Step-by-step solution

The area of a square is equal to the value of one of its sides squared.

Below is the formula for the area of a square:

$S=a^2$

Let's therefore insert the known data into the formula as follows:

$S=\frac{x^2}{y^2}$

Final Answer

$\frac{x^2}{y^2}$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared: A = s²
Technique: If side is x/y, then area is $\frac{x^2}{y^2}$
Check: Verify dimensions match: (length)² gives area units ✓

Common Mistakes

Avoid these frequent errors

Using perimeter formula instead of area formula
Don't add all four sides like 4s = perimeter! This gives you the distance around the square, not the space inside. Always square the side length to find area: A = s².

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

How do I know which expression represents the side length?

Look at the diagram carefully! The side is labeled as x/y, so you need to square this entire expression to get the area.

Why isn't the area just x² or y²?

Because the side length isn't just x or y - it's the fraction x/y. When you square a fraction, you square both the numerator and denominator: $\left(\frac{x}{y}\right)^2 = \frac{x^2}{y^2}$

What's wrong with choosing (y-x)²?

This would only be correct if the side length was (y-x). But from the diagram, the side is x/y, not a difference between y and x.

How do I square a fraction?

When squaring a fraction, square the top and bottom separately: $\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$ . So $\left(\frac{x}{y}\right)^2 = \frac{x^2}{y^2}$

Can I simplify x²/y² further?

Not without knowing specific values for x and y. The expression $\frac{x^2}{y^2}$ is already in its simplest algebraic form.

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