Square Area: Finding the Algebraic Expression for ABCD

Square Area with Algebraic Side Expressions

Look at the following square:

AAABBBDDDCCC

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
00:03 Let's figure out the area of a square.
00:06 We know the side length from the data given.
00:10 To find the area, we use the formula: side length times side length.
00:20 We substitute the values and solve to find the area.
00:25 And there you have it. That's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following square:

AAABBBDDDCCC

Which expression represents its area?

2

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=a2 S=a^2

Hence let's insert the given data into the formula as follows:

S=(x+7y)2 S=(x+7y)^2

3

Final Answer

(x+7y)2 (x+7y)^2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared
  • Technique: If side is x+7y x+7y , then area is (x+7y)2 (x+7y)^2
  • Check: Verify that your expression represents side squared ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to square the entire expression
    Don't just square individual terms like x2+7y2 x^2 + 7y^2 instead of (x+7y)2 (x+7y)^2 ! This misses the cross-multiplication terms and gives an incomplete answer. Always square the complete side expression as one unit.

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 isn't the area just x2+7y2 x^2 + 7y^2 ?

+

Because you must square the entire expression (x+7y) (x+7y) ! When you expand (x+7y)2 (x+7y)^2 , you get x2+14xy+49y2 x^2 + 14xy + 49y^2 , not just the sum of squares.

How do I know which side length to use?

+

In a square, all sides are equal! From the diagram, you can see the side is labeled as x+7y x+7y , so use this expression for your area calculation.

What if I expand (x+7y)2 (x+7y)^2 ?

+

That's fine! (x+7y)2=x2+14xy+49y2 (x+7y)^2 = x^2 + 14xy + 49y^2 . Both the factored form (x+7y)2 (x+7y)^2 and expanded form are correct expressions for the area.

Why can't the answer be 7y2 7y^2 ?

+

Because 7y2 7y^2 ignores the x part of the side length! The complete side is x+7y x+7y , so you must include both terms when squaring.

How do I remember the square area formula?

+

Area = side × side = side². Think of it as: if each side has length s, then the area is . Replace s with your actual side expression!

🌟 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