Calculate Square Area: Finding Expression for Side Length (a-b)

Square Area with Variable Side Lengths

Look at the following square:

AAABBBDDDCCCa-b

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 The side length according to the given data
00:07 We'll use the formula for calculating the area of a square (side squared)
00:13 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 following square:

AAABBBDDDCCCa-b

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

We substitute our values into the formula:

A=(ab)2 A=(a-b)^2

3

Final Answer

(ab)2 (a-b)^2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Square area equals side length squared (A = s²)
  • Technique: Substitute side length: A = (a-b)² with given side
  • Check: Side length (a-b) squared gives area expression (a-b)² ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to square the entire side length expression
    Don't just write a-b = wrong area! This gives you length, not area. Area requires two dimensions multiplied together. Always square the complete side length expression: (a-b)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 do I need parentheses around (a-b)?

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The parentheses are crucial because you must square the entire side length expression. Without them, only the 'b' would be squared, giving you a - b² instead of the correct (a-b)².

What's the difference between (a-b)² and (b-a)²?

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Great question! Since we're squaring, both expressions equal the same value: (a-b)² = (b-a)². However, the problem shows the side as 'a-b', so we use (a-b)² to match.

How do I know this is definitely a square?

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The diagram shows four equal sides and right angles at each corner. All sides are labeled with the same length 'a-b', which confirms it's a square.

Can the side length a-b be negative?

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In geometry, side lengths must be positive. This means a > b in this problem. However, (a-b)² will always be positive regardless!

What if I chose (b-a)² as my answer?

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Mathematically, (b-a)² equals (a-b)² since both are squared. But the correct answer matches the given information in the diagram, which shows the side as 'a-b'.

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