Find the Area Expression for a Square with Vertices ABCD

Q: Why isn't the area just xy if that's the side length?

Because area measures two-dimensional space! You need length × width, and since it's a square, that's side × side. So if side = xy, then area = xy × xy = $ x^2y^2 $.

Q: How do I square a product like xy?

When squaring a product, square each factor separately: $ (xy)^2 = x^2 \times y^2 = x^2y^2 $. Think of it as (x × y) × (x × y).

Q: Could the answer be (x+y)²?

No! That would mean the side length is x+y, not xy. The diagram shows the side as xy (x times y), so we square that: $ (xy)^2 = x^2y^2 $.

Q: How can I remember the square area formula?

Think "side times side" - that's what area means for any rectangle! Since a square has equal sides, it's always side × side = side². If side = xy, then area = xy × xy = $ x^2y^2 $.

Square Area with Variable Side Lengths

Look at the square shown below:

Which expression represents its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the area of the square

00:03 Side length according to the given data

00:07 We'll use the formula for calculating the area of a square (side squared)

00:15 We'll substitute appropriate values and solve to find the area

00:24 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

Look at the square shown below:

Which expression represents its area?

Step-by-step solution

The area of a square can be obtained by squaring the measurement of one of its sides.

The formula for the area of a square is:

$S=a^2$

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

$S=x^2y^2$

Final Answer

$x^2y^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared
Technique: If side is xy, then area = $(xy)^2 = x^2y^2$
Check: Verify units make sense: length × length = area units ✓

Common Mistakes

Avoid these frequent errors

Writing side length instead of side squared
Don't write xy as the area = wrong formula! This gives you perimeter thinking instead of area. Always remember that area requires squaring the side length to get $(xy)^2 = x^2y^2$ .

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square?

FAQ

Everything you need to know about this question

Why isn't the area just xy if that's the side length?

Because area measures two-dimensional space! You need length × width, and since it's a square, that's side × side. So if side = xy, then area = xy × xy = $x^2y^2$ .

How do I square a product like xy?

When squaring a product, square each factor separately: $(xy)^2 = x^2 \times y^2 = x^2y^2$ . Think of it as (x × y) × (x × y).

Could the answer be (x+y)²?

No! That would mean the side length is x+y, not xy. The diagram shows the side as xy (x times y), so we square that: $(xy)^2 = x^2y^2$ .

What if I forgot to square both variables?

That's a common mistake! Remember: when you square a product, every factor gets squared. So $(xy)^2$ becomes $x^2y^2$ , not $xy^2$ or $x^2y$ .

How can I remember the square area formula?

Think "side times side" - that's what area means for any rectangle! Since a square has equal sides, it's always side × side = side². If side = xy, then area = xy × xy = $x^2y^2$ .

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