Calculate the Area of Square ABCD: Geometric Expression Problem

Q: Why can't I just use 36 as the area if I see the number 6?

The side length isn't just 6 - it's 6+4x! The variable x represents an unknown value that changes the actual length. You must include the entire algebraic expression.

Q: Do I need to expand (6+4x)² to find the area?

Not necessarily! The expression $ (6+4x)^2 $ already represents the area perfectly. Expanding would give you $ 36 + 48x + 16x^2 $, but both forms are correct.

Q: How do I know this is really a square from the diagram?

Look for four equal sides and right angles at each corner. The diagram shows all sides labeled with the same expression (6+4x), confirming it's a square.

Q: Can I substitute a number for x to check my answer?

Absolutely! Try x = 1: side length becomes 6+4(1) = 10, so area = 10² = 100. Using our formula: (6+4×1)² = 10² = 100 ✓

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)

00:16 We'll substitute appropriate values and solve to find the area

00:22 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:

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:

$S=(6+4x)^2$

Final Answer

$(6+4x)^2$

Key Points to Remember

Essential concepts to master this topic

Square Area Formula: Area equals side length squared (A = s²)
Algebraic Substitution: Replace s with (6+4x) to get (6+4x)²
Verification: Check that all four sides are equal length ✓

Common Mistakes

Avoid these frequent errors

Using only the numerical part of the side length
Don't calculate area as 6² = 36 ignoring the variable term! This misses the algebraic part completely and gives an incomplete answer. Always use the entire expression (6+4x) as the side length.

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 use 36 as the area if I see the number 6?

The side length isn't just 6 - it's 6+4x! The variable x represents an unknown value that changes the actual length. You must include the entire algebraic expression.

Do I need to expand (6+4x)² to find the area?

Not necessarily! The expression $(6+4x)^2$ already represents the area perfectly. Expanding would give you $36 + 48x + 16x^2$ , but both forms are correct.

How do I know this is really a square from the diagram?

Look for four equal sides and right angles at each corner. The diagram shows all sides labeled with the same expression (6+4x), confirming it's a square.

What if x is negative - can a square have negative area?

Great question! For a square to exist, the side length (6+4x) must be positive. This means x > -1.5. If x makes the side length negative or zero, the square wouldn't exist in reality.

Can I substitute a number for x to check my answer?

Absolutely! Try x = 1: side length becomes 6+4(1) = 10, so area = 10² = 100. Using our formula: (6+4×1)² = 10² = 100 ✓

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