Calculate Square Area: Finding Area When Side Length is (x+y)

Q: Why do I square the entire expression (x+y)?

Because the entire side length is (x+y), not just x or y separately. When you square a side length, you square the complete expression that represents that length.

Q: Should I expand (x+y)² or leave it as is?

For this problem, leave it as $ (x+y)^2 $. The question asks to "express the area," so the factored form is the clearest answer. Expanding would give $ x^2 + 2xy + y^2 $, which is also correct but more complicated.

Q: How is this different from a rectangle?

A square has all sides equal, so you only need one measurement. For rectangles, you multiply length × width. Here, all sides are (x+y), so area = (x+y) × (x+y) = $ (x+y)^2 $.

Q: What if x or y are negative numbers?

The expression $ (x+y)^2 $ will still work! Since we're squaring, the result is always positive. Remember, area must be positive in real-world problems.

Q: Can I use this formula for any square?

Absolutely! The formula $ A = s^2 $ works for any square, where s is the side length. Whether s is a number, variable, or expression like (x+y), just square it!

Square Area with Algebraic Expressions

Look at the following square:

Express the area of the square.

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

00:13 Substitute appropriate values and solve to find the area

00:19 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 following square:

Express the area of the square.

Step-by-step solution

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

Formula for the square area:

$A=L^2$

We substitute our values into the formula:

$A=(x+y)^2$

Final Answer

$(x+y)^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of a square equals side length squared
Technique: Apply formula: $A = (x+y)^2$
Check: Verify units are squared and expression matches square dimensions ✓

Common Mistakes

Avoid these frequent errors

Adding instead of squaring the side length
Don't calculate area as 2(x+y) or x+y = linear result! This gives the perimeter formula or just the side length, not area. Always square the entire side length expression: $(x+y)^2$ .

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 do I square the entire expression (x+y)?

Because the entire side length is (x+y), not just x or y separately. When you square a side length, you square the complete expression that represents that length.

Should I expand (x+y)² or leave it as is?

For this problem, leave it as $(x+y)^2$ . The question asks to "express the area," so the factored form is the clearest answer. Expanding would give $x^2 + 2xy + y^2$ , which is also correct but more complicated.

How is this different from a rectangle?

A square has all sides equal, so you only need one measurement. For rectangles, you multiply length × width. Here, all sides are (x+y), so area = (x+y) × (x+y) = $(x+y)^2$ .

What if x or y are negative numbers?

The expression $(x+y)^2$ will still work! Since we're squaring, the result is always positive. Remember, area must be positive in real-world problems.

Can I use this formula for any square?

Absolutely! The formula $A = s^2$ works for any square, where s is the side length. Whether s is a number, variable, or expression like (x+y), just square it!

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