Rectangle Area: Calculate When One Side is 6cm and Another is 40% Longer

Q: How do I calculate 40% of a number?

Convert the percentage to a decimal: 40% = 0.40, then multiply: $ 0.40 \times 6 = 2.4 $. You can also use the fraction $ \frac{40}{100} = \frac{2}{5} $.

Q: What does '40% longer' actually mean?

40% longer means the new length is the original length plus 40% of the original. So AB = BC + (40% of BC) = 6 + 2.4 = 8.4 cm.

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

Remember: Area = length × width. It doesn't matter which side you call length or width - just multiply the two different side measurements together!

Q: Can I check my percentage calculation another way?

Yes! Think of it as 140% of the original: $ 1.40 \times 6 = 8.4 $. This gives the same result as $ 6 + 0.40 \times 6 $.

Rectangle Area with Percentage Increases

Given below is the rectangle ABCD.

Given in cm: BC = 6

Side AB is 40% longer than side BC.

Calculate the area of the rectangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of the rectangle

00:06 Use the given ratio of sides

00:15 Substitute appropriate values according to the given data, calculate the percentages

00:22 Reduce what can be reduced

00:29 Make sure to multiply numerator by numerator and denominator by denominator

00:47 This is the length of the side

00:56 Use the formula to calculate the area of a rectangle (side times side)

01:03 Substitute appropriate values according to the given data and calculate to find the area

01:13 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 below is the rectangle ABCD.

Given in cm: BC = 6

Side AB is 40% longer than side BC.

Calculate the area of the rectangle.

Step-by-step solution

Let's begin by calculating side AB:

$AB=BC+40\%$

$AB=6+40\%$

$AB=6+\frac{40}{100}\times6$

$AB=6+\frac{4}{10}\times6$

$AB=6+\frac{4\times6}{10}=6+\frac{24}{10}=6+2.4=8.4$

We can now calculate the area of the rectangle by multiplying the length by the width:

$8.4\times6=50.4$

Final Answer

50.4

Key Points to Remember

Essential concepts to master this topic

Percentage Rule: Add the percentage to 100% when finding increases
Technique: Calculate $6 + 40\% \times 6 = 6 + 2.4 = 8.4$
Check: Verify area calculation: $8.4 \times 6 = 50.4 \text{ cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Adding the percentage directly to the base number
Don't add 40 to 6 to get 46! This treats 40% as 40 units instead of 40% of 6. The percentage must be calculated first: 40% of 6 = 2.4, then add to get 6 + 2.4 = 8.4. Always convert the percentage to its decimal value and multiply by the base number.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side AB is 2 cm long and side BC has a length of 7 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

How do I calculate 40% of a number?

Convert the percentage to a decimal: 40% = 0.40, then multiply: $0.40 \times 6 = 2.4$ . You can also use the fraction $\frac{40}{100} = \frac{2}{5}$ .

What does '40% longer' actually mean?

40% longer means the new length is the original length plus 40% of the original. So AB = BC + (40% of BC) = 6 + 2.4 = 8.4 cm.

Why can't I just multiply 6 × 40 to get the area?

That would give you 240, but you're missing the percentage calculation! You need to find the actual length of AB first (8.4 cm), then multiply: 8.4 × 6 = 50.4 cm².

How do I remember the area formula for rectangles?

Remember: Area = length × width. It doesn't matter which side you call length or width - just multiply the two different side measurements together!

Can I check my percentage calculation another way?

Yes! Think of it as 140% of the original: $1.40 \times 6 = 8.4$ . This gives the same result as $6 + 0.40 \times 6$ .

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