Square Area Expression: Finding the Area of Square ABCD

Q: Why can't I just square 9 and y separately?

Because the side length is one expression: (9+y). When you square a sum, you get $ (a+b)^2 = a^2 + 2ab + b^2 $, not just $ a^2 + b^2 $!

Q: How do I know this is definitely a square?

The diagram shows four equal sides and right angles at each corner. The side length is labeled as (9+y), so all four sides have this same measurement.

Q: What if y is negative?

That's fine! As long as (9+y) > 0, we have a valid square. The expression $ (9+y)^2 $ will always give a positive area regardless of y's sign.

Q: Can I use different area formulas for squares?

No, there's only one formula for square area: $ A = s^2 $ where s is the side length. Other formulas like length × width give the same result since length = width in squares.

Square Area with Algebraic Side Lengths

Look at the following square:

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

00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following square:

Which expression represents its area?

Step-by-step solution

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

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(9+y)^2$

Final Answer

$(9+y)^2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of a square equals side length squared
Technique: For side (9+y), area = $(9+y)^2$
Check: Verify the side measurement includes both terms 9 and y ✓

Common Mistakes

Avoid these frequent errors

Using only one part of the side length expression
Don't calculate area as $9^2$ or $y^2$ alone = ignores part of the side! The complete side length is (9+y), so you must square the entire expression. Always square the complete side length: $(9+y)^2$ .

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 can't I just square 9 and y separately?

Because the side length is one expression: (9+y). When you square a sum, you get $(a+b)^2 = a^2 + 2ab + b^2$ , not just $a^2 + b^2$ !

Do I need to expand (9+y)²?

For this problem, no! The question asks for the expression that represents the area. $(9+y)^2$ is the correct expression in its simplest form.

How do I know this is definitely a square?

The diagram shows four equal sides and right angles at each corner. The side length is labeled as (9+y), so all four sides have this same measurement.

What if y is negative?

That's fine! As long as (9+y) > 0, we have a valid square. The expression $(9+y)^2$ will always give a positive area regardless of y's sign.

Can I use different area formulas for squares?

No, there's only one formula for square area: $A = s^2$ where s is the side length. Other formulas like length × width give the same result since length = width in squares.

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