Calculate Rectangle Area: 4-Squared Width × 5cm Length Problem

Q: Do I multiply 4² × 5 or (4²) × 5?

Always evaluate the exponent first! $ 4^2 = 16 $, then multiply: 16 × 5 = 80. The exponent only applies to the 4, not the entire expression.

Q: What does 4² actually mean?

$ 4^2 $ means 4 × 4 = 16. It's called "4 squared" because you multiply 4 by itself once. This gives us the width of 16 cm.

Q: Why is the answer 80 and not 81?

Because $ 4^2 = 16 $ (not 17!), so the calculation is 16 × 5 = 80. Double-check your exponent: 4 × 4 = 16.

Q: What units should my final answer have?

Since you're multiplying cm × cm, the area must be in square centimeters (cm²). Always include the correct units in your final answer!

Q: Can I use the order of operations here?

Yes! Follow PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Evaluate $ 4^2 $ first, then multiply by 5.

Rectangle Area with Exponent Evaluation

The width of a rectangle is equal to $4^2$ cm and its length is $5$ 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 Insert the relevant values according to the given data and proceed to solve for the area

00:10 Calculate 4 squared

00:19 Break down 16 into 10 plus 6

00:22 Open the parentheses properly - multiply each factor

00:33 Calculate each multiplication separately and proceed to add them together

00:37 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 $4^2$ cm and its length is $5$ cm.

Calculate the area of the rectangle.

Step-by-step solution

We use the formula to calculate a rectangle: length times width:

According to the existing data:

$4^2\times5^=S$

$S=16\times5$

$S=80$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width
Technique: Calculate $4^2 = 16$ first, then multiply by 5
Check: Verify dimensions make sense: 16 cm × 5 cm = 80 cm² ✓

Common Mistakes

Avoid these frequent errors

Forgetting to evaluate the exponent first
Don't multiply 4 × 5 directly = 20 wrong answer! This skips the crucial exponent step and gives the wrong width. Always evaluate $4^2 = 16$ first, then multiply 16 × 5.

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

Do I multiply 4² × 5 or (4²) × 5?

Always evaluate the exponent first! $4^2 = 16$ , then multiply: 16 × 5 = 80. The exponent only applies to the 4, not the entire expression.

What does 4² actually mean?

$4^2$ means 4 × 4 = 16. It's called "4 squared" because you multiply 4 by itself once. This gives us the width of 16 cm.

Why is the answer 80 and not 81?

Because $4^2 = 16$ (not 17!), so the calculation is 16 × 5 = 80. Double-check your exponent: 4 × 4 = 16.

What units should my final answer have?

Since you're multiplying cm × cm, the area must be in square centimeters (cm²). Always include the correct units in your final answer!

Can I use the order of operations here?

Yes! Follow PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Evaluate $4^2$ first, then multiply by 5.

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