Calculate Square Area: Finding Area When Side Length is X-7

Area Formula with Algebraic Side Lengths

Look at the square below:

AAABBBDDDCCCX-7

Express its area in terms of x x .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's express the area of the square.
00:07 Remember, the side length depends on the data given.
00:11 We use the formula: area equals side length, times side length.
00:17 Substitute the values, solve, and you'll find the area.
00:27 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:

AAABBBDDDCCCX-7

Express its area in terms of x x .

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.

The formula for the area of the square is

A=L2 A=L^2

We place the data in the formula:

A=(x7)2 A=(x-7)^2

3

Final Answer

(x7)2 (x-7)^2

Key Points to Remember

Essential concepts to master this topic
  • Square Area Rule: Area equals side length squared, A = s²
  • Algebraic Technique: Substitute (x-7) for side length: A = (x-7)²
  • Verification Check: If x = 10, then area = (10-7)² = 9 square units ✓

Common Mistakes

Avoid these frequent errors
  • Adding 2 to the side length instead of squaring
    Don't write (x-7) + 2 or 2(x-7) = wrong area formula! This gives a linear expression, not area. Always remember that area means multiply the side by itself: (x-7) × (x-7) = (x-7)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 can't I just write x² - 7² as the area?

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That's not how algebra works! The side length is the entire expression (x-7), not x and 7 separately. You must square the whole thing: (x7)2 (x-7)^2 , not individual parts.

Do I need to expand (x-7)² into x² - 14x + 49?

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Not unless asked! The question asks to express the area in terms of x, and (x7)2 (x-7)^2 is already a perfect expression. Keep it simple and factored.

What if x is less than 7? Can a square have negative side length?

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Great question! In real geometry, side lengths must be positive, so x > 7. But in algebra problems, we often work with expressions even when they might not make physical sense.

How do I check if my area formula is correct?

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Pick a test value! If x = 10, then side = 10-7 = 3, so area = 3² = 9. Your formula should give: (107)2=32=9 (10-7)^2 = 3^2 = 9

Is there a difference between (x-7)² and (-7+x)²?

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No difference at all! Both expressions are equal because addition is commutative. So (x-7)² = (-7+x)² = (x-7)². Use whichever form looks cleaner to you.

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