Square with Side Length 4: Comparing Perimeter vs Area

Q: Why are the area and perimeter the same for this square?

This is a special case! When the side length is 4, both $ 4^2 = 16 $ and $ 4 \times 4 = 16 $. For other side lengths, area and perimeter will be different values.

Q: What's the difference between area and perimeter?

Area measures the space inside the square (square units), while perimeter measures the distance around the square (linear units). They measure completely different things!

Q: How do I remember which formula to use?

Think about what you're measuring: Area fills up space (like tiles), so multiply length × width = side². Perimeter goes around the edge (like a fence), so add all four sides = 4 × side.

Q: What if the side length was 3 or 5 instead?

Let's see: For side 3, area = $ 3^2 = 9 $ and perimeter = $ 4 \times 3 = 12 $. For side 5, area = $ 5^2 = 25 $ and perimeter = $ 4 \times 5 = 20 $. They're different!

Square Properties with Equal Measurements

Look at the square below:

Is the perimeter of the square greater than its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Is the perimeter of the square greater than its area?

00:03 The side length according to the given data

00:07 The perimeter of the square equals the sum of its sides

00:11 We'll substitute appropriate values and solve to find the perimeter

00:14 This is the perimeter of the square

00:19 We'll use the formula for calculating the area of a square (side squared)

00:23 We'll substitute appropriate values and solve to find the area

00:30 According to our calculation, the square's perimeter and area are equal

00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the square below:

Is the perimeter of the square greater than its area?

Step-by-step solution

Let's remember that the area of the square is equal to the side of the square raised to the second power.

Let's remember that the perimeter of the square is equal to the side multiplied by 4.

We calculate the area of the square:

$A=4^2=16$

We calculate the perimeter of the square:

$4\times4=16$

Therefore, the perimeter is not greater than the area (they are equal).

Final Answer

False

Key Points to Remember

Essential concepts to master this topic

Formula: Area = side², Perimeter = 4 × side
Calculation: For side 4: Area = 4² = 16, Perimeter = 4 × 4 = 16
Check: Compare values directly: 16 = 16, so perimeter equals area ✓

Common Mistakes

Avoid these frequent errors

Forgetting to square the side length for area
Don't calculate area as 4 × 4 = 16 thinking it's the same as perimeter! This confuses multiplication with squaring. Always remember area uses side² (4² = 4 × 4 = 16) while perimeter uses 4 × side.

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

Why are the area and perimeter the same for this square?

This is a special case! When the side length is 4, both $4^2 = 16$ and $4 \times 4 = 16$ . For other side lengths, area and perimeter will be different values.

What's the difference between area and perimeter?

Area measures the space inside the square (square units), while perimeter measures the distance around the square (linear units). They measure completely different things!

For what other side lengths are area and perimeter equal?

Only when the side length is 4! For any square with side s, area = perimeter when $s^2 = 4s$ , which gives us $s = 4$ (or $s = 0$ , but that's not a real square).

How do I remember which formula to use?

Think about what you're measuring: Area fills up space (like tiles), so multiply length × width = side². Perimeter goes around the edge (like a fence), so add all four sides = 4 × side.

What if the side length was 3 or 5 instead?

Let's see: For side 3, area = $3^2 = 9$ and perimeter = $4 \times 3 = 12$ . For side 5, area = $5^2 = 25$ and perimeter = $4 \times 5 = 20$ . They're different!

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Square with Side Length 4: Comparing Perimeter vs Area

Square Properties with Equal Measurements

❤️ 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

Why are the area and perimeter the same for this square?

What's the difference between area and perimeter?

For what other side lengths are area and perimeter equal?

How do I remember which formula to use?

What if the side length was 3 or 5 instead?

🌟 Unlock Your Math Potential

More Questions

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Compare Perimeter vs Area: 5-Unit Square Analysis

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