Calculate Rectangle Area: 3² cm Width × 1.5 cm Length

Q: Why do I need to calculate the exponent first?

Order of operations requires calculating exponents before multiplication! $ 3^2 $ means 3 × 3 = 9, so the actual width is 9 cm, not 3 cm.

Q: How do I multiply a whole number by a decimal?

Multiply normally, then count decimal places. $ 9 \times 1.5 $: Think of it as 9 × 15 = 135, then move the decimal one place left to get 13.5.

Q: What does cm² mean in the answer?

$ \text{cm}^2 $ means square centimeters - the unit for area. When you multiply length × width, you multiply the units too: cm × cm = cm².

Q: What if the exponent was different, like 3³?

Same process! Calculate the exponent first: $ 3^3 = 3 \times 3 \times 3 = 27 $, then multiply by the length. Always handle exponents before using the number in other calculations.

Rectangle Area with Exponents

The width of a rectangle is equal to $3^2$ cm and its length is $1.5~$ cm.

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 rectangle's area

00:03 Apply the formula for calculating the area of a rectangle (side x side)

00:07 Substitute in the relevant values according to the given data and proceed to solve for the area

00:20 Break down 1.5 into 1 and a half

00:23 Expand the brackets - multiply each factor

00:32 Calculate each multiplication and then add them together

00:40 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The width of a rectangle is equal to $3^2$ cm and its length is $1.5~$ cm.

Calculate the area of the rectangle.

Step-by-step solution

Let's begin by solving the first exercise:

$3^2=9$

Now let's multiply the length by the width in order to find the area of the rectangle:

$9\times1.5=13.5$

Final Answer

13.5

Key Points to Remember

Essential concepts to master this topic

Exponents First: Calculate $3^2 = 9$ before using in area formula
Area Formula: Area = width × length = $9 \times 1.5 = 13.5$ square cm
Check Units: Width (9 cm) × length (1.5 cm) = 13.5 cm² ✓

Common Mistakes

Avoid these frequent errors

Using 3 instead of calculating 3²
Don't use 3 × 1.5 = 4.5! This ignores the exponent completely. The width is 3² = 9 cm, not 3 cm. Always calculate exponents first before applying formulas.

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

Why do I need to calculate the exponent first?

Order of operations requires calculating exponents before multiplication! $3^2$ means 3 × 3 = 9, so the actual width is 9 cm, not 3 cm.

How do I multiply a whole number by a decimal?

Multiply normally, then count decimal places. $9 \times 1.5$ : Think of it as 9 × 15 = 135, then move the decimal one place left to get 13.5.

What does cm² mean in the answer?

$\text{cm}^2$ means square centimeters - the unit for area. When you multiply length × width, you multiply the units too: cm × cm = cm².

Can I check my answer somehow?

Yes! Make sure your area makes sense: a rectangle that's 9 cm by 1.5 cm should have an area between 9 and 18 cm². Since 13.5 falls in this range, it's reasonable!

What if the exponent was different, like 3³?

Same process! Calculate the exponent first: $3^3 = 3 \times 3 \times 3 = 27$ , then multiply by the length. Always handle exponents before using the number in other calculations.

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