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 ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area 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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