Calculate Area: Square with Sides 5 Units Longer

Q: Why can't I just add 5 to the original area of 25?

Because area and side length are different measurements! The problem says the sides are 5 units longer, not the area. You must first find the new side length (5 + 5 = 10), then calculate the new area (10² = 100).

Q: What's the difference between adding to sides vs. adding to area?

Adding to sides: $ (5+5)^2 = 10^2 = 100 $Adding to area: $ 5^2 + 5 = 25 + 5 = 30 $ (WRONG!)The side length change has a much bigger effect on area because of squaring.

Q: How do I remember the area formula for squares?

Think of it as "side times side" or $ s^2 $. A square with side 10 has 10 rows of 10 small squares each, giving 10 × 10 = 100 total squares!

Q: What if the sides were shorter instead of longer?

Same process! If sides were 5 units shorter, the new side would be 5 - 5 = 0. Then area = $ 0^2 = 0 $. Always change the side length first, then square it for area.

Q: Why is the answer 100 and not 50?

Because area involves squaring! When you double the side length (from 5 to 10), you actually quadruple the area (from 25 to 100). This is why $ 10^2 = 100 $, not 50.

Square Area Calculations with Side Length Changes

Given a square whose sides are 5. We draw another square whose sides are longer by 5 than the length of the sides of the previous square. Find the area of the new square.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of the new square

00:03 The given square's side length

00:06 The new square's side is 5 times larger than the given one

00:10 Let's calculate the side length of the new square

00:14 We'll use the formula for square area (side squared)

00:18 We'll substitute appropriate values and solve for 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

Given a square whose sides are 5. We draw another square whose sides are longer by 5 than the length of the sides of the previous square. Find the area of the new square.

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Determine the side length of the new square.
Step 2: Calculate the area of the new square using the area formula for a square.

Now, let's work through the solution:

Step 1: Calculate the side length of the new square.

The side length of the original square is 5 units. The problem states that the side of the new square is longer by 5 units than the original square. Therefore, the side length of the new square is:

$\text{New Side Length} = 5 + 5 = 10 \text{ units}$

Step 2: Calculate the area of the new square.

To find the area of the new square, we use the formula for the area of a square, which is the side length squared:

$\text{Area of the New Square} = (\text{Side Length})^2 = 10^2 = 100 \text{ square units}$

Therefore, the area of the new square is 100 square units.

Thus, the correct answer is option 3: 100.

Final Answer

100

Key Points to Remember

Essential concepts to master this topic

Formula: Area of square equals side length squared
Technique: New side = 5 + 5 = 10, so area = 10² = 100
Check: Verify 10 × 10 = 100 square units ✓

Common Mistakes

Avoid these frequent errors

Adding 5 to the area instead of the side length
Don't add 5 to the original area (25 + 5 = 30) = completely wrong answer! This confuses area with side length. Always add the given amount to the side length first, then square the new side length to find the area.

Practice Quiz

Test your knowledge with interactive questions

$$ 11^2= $$

FAQ

Everything you need to know about this question

Why can't I just add 5 to the original area of 25?

Because area and side length are different measurements! The problem says the sides are 5 units longer, not the area. You must first find the new side length (5 + 5 = 10), then calculate the new area (10² = 100).

What's the difference between adding to sides vs. adding to area?

Adding to sides: $(5+5)^2 = 10^2 = 100$
Adding to area: $5^2 + 5 = 25 + 5 = 30$ (WRONG!)
The side length change has a much bigger effect on area because of squaring.

How do I remember the area formula for squares?

Think of it as "side times side" or $s^2$ . A square with side 10 has 10 rows of 10 small squares each, giving 10 × 10 = 100 total squares!

What if the sides were shorter instead of longer?

Same process! If sides were 5 units shorter, the new side would be 5 - 5 = 0. Then area = $0^2 = 0$ . Always change the side length first, then square it for area.

Why is the answer 100 and not 50?

Because area involves squaring! When you double the side length (from 5 to 10), you actually quadruple the area (from 25 to 100). This is why $10^2 = 100$ , not 50.

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Calculate Area: Square with Sides 5 Units Longer

Square Area Calculations with Side Length Changes

❤️ 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 can't I just add 5 to the original area of 25?

What's the difference between adding to sides vs. adding to area?

How do I remember the area formula for squares?

What if the sides were shorter instead of longer?

Why is the answer 100 and not 50?

🌟 Unlock Your Math Potential

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