Calculate the Area of Square ABCD: Using Geometric Formulas

Q: Why don't I need to expand (2+x)²?

The question asks for the expression that describes the area, not the expanded form. $ (2+x)^2 $ is the correct expression, even though it could be expanded to $ 4 + 4x + x^2 $.

Q: What if the side length had subtraction like (2-x)?

The same rule applies! The area would be $ (2-x)^2 $. Always square the entire expression that represents the side length, whether it has addition or subtraction.

Q: How is this different from a rectangle?

In a square, all four sides are equal, so you only need one side measurement. For a rectangle, you'd need length × width since the sides are different lengths.

Q: What if I see negative signs in the answer choices?

Be careful with signs! $ (-2+x)^2 $ and $ (x-2)^2 $ are the same, but $ (-2-x)^2 $ is different. Always match the exact form of the side length from the diagram.

Square Area Formula with Variable Expressions

Look at the square below:

Which expression describes its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find the area of the square.

00:06 First, look at the side length given to us.

00:10 We use the formula: the side of the square, times itself, or side squared.

00:16 Now, let's put in the values and calculate the area. You're doing great!

00:21 And that's how we solve this problem. Well done!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the square below:

Which expression describes 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:

$S=(2+x)^2$

Final Answer

$(2+x)^2$

Key Points to Remember

Essential concepts to master this topic

Area Formula: Square area equals side length squared: $A = s^2$
Technique: Identify side length from diagram, then square the entire expression
Check: Verify the expression matches the squared side length shown ✓

Common Mistakes

Avoid these frequent errors

Squaring only part of the side expression
Don't square just the number or just the variable when the side is (2+x) = incorrect result! This gives expressions like 4+x² instead of the full expansion. Always square the complete binomial expression using $(a+b)^2 = a^2 + 2ab + b^2$ .

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

What is the area of the square?

FAQ

Everything you need to know about this question

How do I identify the side length from the diagram?

Look at the labels on the sides of the square. In this problem, the side length is shown as 2+x, which appears to be marked along one edge of the square.

Why don't I need to expand (2+x)²?

The question asks for the expression that describes the area, not the expanded form. $(2+x)^2$ is the correct expression, even though it could be expanded to $4 + 4x + x^2$ .

What if the side length had subtraction like (2-x)?

The same rule applies! The area would be $(2-x)^2$ . Always square the entire expression that represents the side length, whether it has addition or subtraction.

How is this different from a rectangle?

In a square, all four sides are equal, so you only need one side measurement. For a rectangle, you'd need length × width since the sides are different lengths.

What if I see negative signs in the answer choices?

Be careful with signs! $(-2+x)^2$ and $(x-2)^2$ are the same, but $(-2-x)^2$ is different. Always match the exact form of the side length from the diagram.

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Calculate the Area of Square ABCD: Using Geometric Formulas

Square Area Formula with Variable Expressions

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I identify the side length from the diagram?

Why don't I need to expand (2+x)²?

What if the side length had subtraction like (2-x)?

How is this different from a rectangle?

What if I see negative signs in the answer choices?

🌟 Unlock Your Math Potential

More Questions

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Square Area: Finding the Geometric Expression for ABCD

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Square Area: Finding the Algebraic Expression for ABCD

Square Area Expression: Finding the Area of Square ABCD