Calculate Square Area: Finding Area When Side Length is (4+X)

Square Area with Algebraic Expressions

Look at the square below:

AAABBBDDDCCC4+X

Which expression represents its area?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Express the area of the square
00:03 The side length according to the given data
00:07 We'll use the formula for calculating the area of a square (side squared)
00:14 We'll substitute appropriate values and solve to find the area
00:21 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

AAABBBDDDCCC4+X

Which expression represents its area?

2

Step-by-step solution

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

Formula for the area of the square:

A=L2 A=L^2

Then we substitute our values into the formula:

A=(4+x)2 A=(4+x)^2

3

Final Answer

(4+x)2 (4+x)^2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared
  • Technique: Substitute (4+x) into A = L²: A = (4+x)²
  • Check: Keep parentheses - don't expand unless specifically asked ✓

Common Mistakes

Avoid these frequent errors
  • Trying to expand (4+x)² instead of keeping it factored
    Don't expand (4+x)² = 16 + 8x + x² when the question asks for the expression! This makes it more complicated and isn't what's being asked. Always read carefully - if they want the expression for area, keep it as (4+x)².

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

111111

What is the area of the square?

FAQ

Everything you need to know about this question

Why don't I expand (4+x)² into 16 + 8x + x²?

+

The question asks for the expression that represents the area. (4+x)2 (4+x)^2 is already a perfectly valid expression! Expanding it would make it longer without being more correct.

How do I know this is definitely a square?

+

Look at the diagram - all four sides are equal, and all corners are right angles. Plus, the side length is labeled as 4+x on just one side, indicating all sides have this same length.

What if x is negative? Does the formula still work?

+

Yes! The formula A=(4+x)2 A = (4+x)^2 works for any value of x. Just remember that area must always be positive, so 4+x must be positive for the square to exist.

Can I write this as (x+4)² instead?

+

Absolutely! Addition is commutative, so (4+x)2 (4+x)^2 and (x+4)2 (x+4)^2 are exactly the same. Both expressions are correct!

Why is the answer not just 4²?

+

Because the side length isn't just 4 - it's 4+x. The variable x could represent any number, so we need to include it in our area calculation. If x=0, then yes, the area would be 4² = 16.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Square for 9th Grade questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations