Compare Square Areas: 6 vs 7 Side Length Analysis

Area Calculation with Side Length Comparison

Given that the length of the sides of square 1 is 6

and the length of the side of square 2 is 7.

Which square has the larger area, 1 or 2?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Which square has a larger area?
00:12 To find the area, we use the formula: side times side.
00:17 Now, we'll plug in the values and solve for the area.
00:20 Here, we have the area of square one.
00:23 Next, let's apply the same steps for square two.
00:29 Let's compare them to see which area is bigger.
00:34 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

Given that the length of the sides of square 1 is 6

and the length of the side of square 2 is 7.

Which square has the larger area, 1 or 2?

2

Step-by-step solution

To solve this problem, we will calculate the area of each square and compare them:

  • Step 1: Calculate the area of square 1.
  • Step 2: Calculate the area of square 2.
  • Step 3: Compare the areas to find which square has a larger area.

Let's work through these steps:

Step 1:

The area of a square is calculated using the formula:

Area=side length2 \text{Area} = \text{side length}^2

For square 1, the side length is 6:

Area1=62=36 \text{Area}_1 = 6^2 = 36

Step 2:

For square 2, the side length is 7:

Area2=72=49 \text{Area}_2 = 7^2 = 49

Step 3:

Now, compare the two areas:

36 36 (Area of square 1) is less than 49 49 (Area of square 2).

Therefore, square 2 has a larger area.

Based on our calculations, the square with the larger area is square 2.

3

Final Answer

2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of square equals side length squared
  • Technique: Calculate 62=36 6^2 = 36 and 72=49 7^2 = 49
  • Check: Compare final areas: 36 < 49, so square 2 is larger ✓

Common Mistakes

Avoid these frequent errors
  • Comparing side lengths instead of areas
    Don't just compare 6 vs 7 and stop there = you're not answering the question about areas! Side length only tells you which square is wider, not which has more space inside. Always calculate the actual areas using the formula Area = side².

Practice Quiz

Test your knowledge with interactive questions

\( 11^2= \)

FAQ

Everything you need to know about this question

Why can't I just compare the side lengths directly?

+

The question asks for area comparison, not side length! While 7 > 6 for sides, you must calculate the actual areas: 62=36 6^2 = 36 and 72=49 7^2 = 49 .

What's the difference between side length and area?

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Side length is the distance along one edge (measured in units like cm). Area is the space inside the square (measured in square units like cm²). Area grows much faster than side length!

Why do I square the side length?

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A square has equal length and width. To find area, you multiply length × width. Since both are the same value, you get side × side = side². That's why we square it!

How much bigger is square 2's area compared to square 1?

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Square 2 has area 49 and square 1 has area 36. The difference is 13 square units. You can also say square 2's area is about 1.36 times larger than square 1's area.

Do I need to include units in my answer?

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The question doesn't specify units, so just the numbers are fine. But remember that areas are measured in square units (like cm² or m²) in real-world problems.

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