Calculate Rectangle Area: Width x² and Length x When x=9

Q: Why do I multiply x by x² instead of adding them?

Area is always length × width, not length + width. Think of it as counting squares: if you have 9 rows of 81 squares each, you multiply to get the total: $ 9 \times 81 = 729 $ square units.

Q: What does x² mean when x = 9?

$ x^2 $ means x squared or x × x. So when x = 9, we get $ 9^2 = 9 \times 9 = 81 $. This is the width of our rectangle.

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

In rectangle area problems, it doesn't matter! Area = length × width = width × length. The multiplication is the same either way: $ 9 \times 81 = 81 \times 9 = 729 $.

Q: What if x was a different number?

The same process works! If x = 5, then width = $ 5^2 = 25 $ and length = 5, so area = $ 5 \times 25 = 125 $. Always substitute first, then multiply.

Rectangle Area with Algebraic Expressions

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

$x=9$

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

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

00:07 Insert the relevant values into the formula according to the given data and solve for the area

00:12 Substitute in the X value according to the given data and proceed to solve

00:16 Break down 9 into its cube factors and solve

00:29 We'll use long multiplication in order to determine the rectangle's area

00:35 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 $x^2$ cm and its length is $x$ cm.

$x=9$

Calculate the area of the rectangle.

Step-by-step solution

The area of a rectangle is equal to length multiplied by width

Let's input the known data into the formula:

$S=x\times x^2$

Since we are given that x equals 9, let's substitute it into the formula:

$S=9\times9^2=9\times81=729$

Final Answer

729

Key Points to Remember

Essential concepts to master this topic

Formula: Rectangle area equals length times width (L × W)
Substitution: Replace x with 9: $9 \times 9^2 = 9 \times 81 = 729$
Check: Verify dimensions make sense: width = 81cm, length = 9cm ✓

Common Mistakes

Avoid these frequent errors

Adding instead of multiplying dimensions
Don't calculate x + x² = 9 + 81 = 90! This gives perimeter-like thinking, not area. Area requires multiplication of dimensions. Always multiply length × width for rectangle area.

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 multiply x by x² instead of adding them?

Area is always length × width, not length + width. Think of it as counting squares: if you have 9 rows of 81 squares each, you multiply to get the total: $9 \times 81 = 729$ square units.

What does x² mean when x = 9?

$x^2$ means x squared or x × x. So when x = 9, we get $9^2 = 9 \times 9 = 81$ . This is the width of our rectangle.

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

In rectangle area problems, it doesn't matter! Area = length × width = width × length. The multiplication is the same either way: $9 \times 81 = 81 \times 9 = 729$ .

Can I check my answer by drawing the rectangle?

Absolutely! Draw a rectangle and label the sides. Width = 81 cm and length = 9 cm. The area should be 729 square cm - that's a lot of little squares!

What if x was a different number?

The same process works! If x = 5, then width = $5^2 = 25$ and length = 5, so area = $5 \times 25 = 125$ . Always substitute first, then multiply.

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