Calculate Rectangle Area: Side Length 9cm with 35% Longer Base

Q: How do I convert 35% to use in calculations?

Convert percentages to decimals by dividing by 100. So 35% = 35 ÷ 100 = 0.35. Then multiply: $ 0.35 \times 9 = 3.15 $

Q: Why do I add the percentage increase to the original length?

Because AB is 35% longer than AD, not just 35% of AD. The new length is: original + increase = 9 + 3.15 = 12.15 cm

Q: What if the question said '35% shorter' instead?

Then you'd subtract the percentage: AB = 9 - (35% × 9) = 9 - 3.15 = 5.85 cm. The word 'longer' means add, 'shorter' means subtract.

Q: How do I know which side is length and which is width?

For rectangles, it doesn't matter! Area = side₁ × side₂ regardless of which you call length or width. The result is the same: 12.15 × 9 = 109.35 cm²

Q: Can I check my percentage calculation?

Yes! 35% of 9 should be about 1/3 of 9 ≈ 3. Since 3.15 is close to 3, your calculation is reasonable. Always do quick estimates!

Rectangle Area with Percentage Length Increases

Rectangle ABCD is shown below.

AD = 9 cm
Side AB is 35% longer than side AD.

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 rectangle ABCD

00:04 The formula for calculating rectangle area is side(AB) multiplied by side (AD)

00:16 Side length according to the given data

00:21 Let's substitute appropriate values and solve for AB

00:30 Convert the percentage to fractions and multiply by the number itself

00:39 This is how we convert percentages to a calculatable number

00:48 We'll move the 9 to the numerator and solve

01:03 This is the length of side AB

01:17 Now we can substitute values in the area formula and solve

01:35 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

Rectangle ABCD is shown below.

AD = 9 cm
Side AB is 35% longer than side AD.

Calculate the area of the rectangle.

Step-by-step solution

First, let's find the length of side AB:

$AB=AD+35\%$

$AB=9+35\%$

$AB=9+\frac{35}{100}\times9$

$AB=9+\frac{35\times9}{100}$

$AB=9+\frac{315}{100}$

$AB=9+3.15=12.15$

Now we can calculate the area of the rectangle by multiplying the length by the width:

$12.15\times9=109.35$

Final Answer

109.35

Key Points to Remember

Essential concepts to master this topic

Percentage Formula: New length = original + (percentage × original)
Calculation: AB = 9 + (35% × 9) = 9 + 3.15 = 12.15 cm
Check: Area = length × width = 12.15 × 9 = 109.35 cm² ✓

Common Mistakes

Avoid these frequent errors

Adding percentage directly to original number
Don't calculate AB = 9 + 35 = 44 cm! This treats 35% as 35 whole units instead of 35% of 9. Always convert the percentage to a decimal first: 35% = 0.35, then multiply by the original value.

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 convert 35% to use in calculations?

Convert percentages to decimals by dividing by 100. So 35% = 35 ÷ 100 = 0.35. Then multiply: $0.35 \times 9 = 3.15$

Why do I add the percentage increase to the original length?

Because AB is 35% longer than AD, not just 35% of AD. The new length is: original + increase = 9 + 3.15 = 12.15 cm

What if the question said '35% shorter' instead?

Then you'd subtract the percentage: AB = 9 - (35% × 9) = 9 - 3.15 = 5.85 cm. The word 'longer' means add, 'shorter' means subtract.

How do I know which side is length and which is width?

For rectangles, it doesn't matter! Area = side₁ × side₂ regardless of which you call length or width. The result is the same: 12.15 × 9 = 109.35 cm²

Can I check my percentage calculation?

Yes! 35% of 9 should be about 1/3 of 9 ≈ 3. Since 3.15 is close to 3, your calculation is reasonable. Always do quick estimates!

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