Calculate Parallelogram Area: 12 cm Width and 4 cm Height Problem

Q: What's the difference between height and side length in a parallelogram?

The height is the perpendicular distance between parallel sides, while side length is the actual length of the slanted side. Always use height for area calculations!

Q: How do I know which measurement is the height?

Look for the perpendicular line in the diagram - it forms a 90° angle with the base. In this problem, the vertical line showing 4 cm is the height.

Q: Why can't I use the slanted side as height?

The slanted side is longer than the perpendicular height. Using it would give you a larger area than the parallelogram actually has!

Q: Do I always multiply base times height?

Yes! The area formula $ \text{Area} = \text{base} \times \text{height} $ works for all parallelograms, including rectangles and squares.

Q: What units should my answer have?

Since you're multiplying two lengths, the area will be in square units. Here: cm × cm = $ \text{cm}^2 $

Q: Can I use any side as the base?

Yes, but then you must use the perpendicular height to that chosen base. The area will always be the same regardless of which side you choose as base!

Area Formula with Base and Height

AB = 12 cm

The height of the rectangle is 4 cm.

Calculate the area of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of parallelogram ABCD

00:03 Opposite sides are equal in a parallelogram

00:14 Let's use the formula for calculating the area of a parallelogram

00:18 Side(CD) multiplied by height (H)

00:23 Let's substitute the appropriate values and solve for the area

00:34 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

AB = 12 cm

The height of the rectangle is 4 cm.

Calculate the area of the parallelogram.

Step-by-step solution

To solve this problem, we'll proceed as follows:

Step 1: Identify the given values for the base and the height of the parallelogram.
Step 2: Apply the formula for calculating the area of the parallelogram.
Step 3: Calculate the area using the values provided.

Let's perform each step:

Step 1: From the problem, we know:

The base $AB$ of the parallelogram is $12 \, \text{cm}$ .
The height relative to the base is $4 \, \text{cm}$ .

Step 2: Use the formula for the area of a parallelogram:

$\text{Area} = \text{base} \times \text{height}$

Step 3: Plugging in the values of the base and height:

$\text{Area} = 12 \times 4 = 48 \, \text{cm}^2$

Therefore, the area of the parallelogram is $48 \, \text{cm}^2$ .

Since this is a multiple-choice problem, the correct answer is Choice 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Parallelogram area equals base times perpendicular height
Technique: Always use perpendicular height: $12 \times 4 = 48$
Check: Verify units are squared and height is perpendicular ✓

Common Mistakes

Avoid these frequent errors

Using slant height instead of perpendicular height
Don't use the slanted side length as height = wrong area calculation! The slant side is longer than the perpendicular height, leading to an overestimated area. Always use the perpendicular distance between parallel sides as your height measurement.

Practice Quiz

Test your knowledge with interactive questions

A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

FAQ

Everything you need to know about this question

What's the difference between height and side length in a parallelogram?

The height is the perpendicular distance between parallel sides, while side length is the actual length of the slanted side. Always use height for area calculations!

How do I know which measurement is the height?

Look for the perpendicular line in the diagram - it forms a 90° angle with the base. In this problem, the vertical line showing 4 cm is the height.

Why can't I use the slanted side as height?

The slanted side is longer than the perpendicular height. Using it would give you a larger area than the parallelogram actually has!

Do I always multiply base times height?

Yes! The area formula $\text{Area} = \text{base} \times \text{height}$ works for all parallelograms, including rectangles and squares.

What units should my answer have?

Since you're multiplying two lengths, the area will be in square units. Here: cm × cm = $\text{cm}^2$

Can I use any side as the base?

Yes, but then you must use the perpendicular height to that chosen base. The area will always be the same regardless of which side you choose as base!

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