Calculate Rectangle Area: 18 cm Width × 2 cm Length Problem

Q: Why do we multiply length and width instead of adding them?

Area measures the space inside the rectangle. When you multiply 2 × 18, you're finding how many unit squares fit inside. Adding gives you the perimeter (distance around the edge) instead.

Q: Does it matter which dimension I call length vs width?

No! Rectangle area is commutative, meaning 2 × 18 = 18 × 2 = 36. The result is the same regardless of which dimension you multiply first.

Q: Why are the units 'square centimeters'?

Area units are always squared because you multiply two lengths together. When you multiply cm × cm, you get cm² (square centimeters).

Q: How can I visualize this rectangle?

Picture a rectangle that's very wide but short - 18 cm across but only 2 cm tall. It's like a long, thin strip that covers 36 square centimeters of space.

Rectangle Area with Length-Width Multiplication

The width of a rectangle is equal to $18$ cm and its length is $2~$ 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)

00:06 Substitute in the relevant values according to the given data and proceed to solve to find the area

00:09 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 $18$ cm and its length is $2~$ cm.

Calculate the area of the rectangle.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: The problem gives us the width, $W = 18$ cm, and the length, $L = 2$ cm.

Step 2: We'll use the formula for the area of a rectangle: $\text{Area} = \text{Length} \times \text{Width}$

Step 3: Plugging in the values, we get: $\text{Area} = 2 \times 18 = 36 \text{ square centimeters}$

Therefore, the area of the rectangle is $36$ square centimeters.

In the provided answer choices, the correct choice is:

Choice 3: $36$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals length times width for all rectangles
Calculation: $2 \times 18 = 36$ square centimeters
Check: Units should be square cm, and 36 is reasonable for these dimensions ✓

Common Mistakes

Avoid these frequent errors

Adding dimensions instead of multiplying
Don't add 18 + 2 = 20! This gives the perimeter formula, not area. Area measures space inside the rectangle, which requires multiplication. Always multiply length × width for area.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do we multiply length and width instead of adding them?

Area measures the space inside the rectangle. When you multiply 2 × 18, you're finding how many unit squares fit inside. Adding gives you the perimeter (distance around the edge) instead.

Does it matter which dimension I call length vs width?

No! Rectangle area is commutative, meaning 2 × 18 = 18 × 2 = 36. The result is the same regardless of which dimension you multiply first.

Why are the units 'square centimeters'?

Area units are always squared because you multiply two lengths together. When you multiply cm × cm, you get cm² (square centimeters).

How can I visualize this rectangle?

Picture a rectangle that's very wide but short - 18 cm across but only 2 cm tall. It's like a long, thin strip that covers 36 square centimeters of space.

What if I accidentally use the perimeter formula?

If you add the dimensions (18 + 2 = 20), you're finding part of the perimeter. The full perimeter would be 2(18 + 2) = 40 cm, which measures distance around the edge, not area inside.

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