Calculate Parallelogram Area: 32cm Width and 15cm Height Problem

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

Height is the perpendicular distance between parallel sides, while side length is measured along the slanted edge. In this problem, height = 15 cm is the vertical distance, not the slanted side.

Q: Why do we use base × height instead of length × width?

A parallelogram is not a rectangle! Length × width only works for rectangles. For parallelograms, we need base × perpendicular height because the sides are slanted.

Q: How do I identify which measurement is the base?

Any side can be the base! In this problem, AB = 32 cm is given as the base. The height (15 cm) is always perpendicular to whichever side you choose as base.

Q: What units should my answer have?

Area is always measured in square units. Since the measurements are in centimeters, your answer should be in square centimeters or cm².

Q: Can I use any parallelogram side as the base?

Yes! You can use any side as the base, but then you must use the height that's perpendicular to that specific side. The area will be the same regardless of which side you choose.

Area of Parallelogram with Base-Height Formula

AB = 32 cm

The height of the rectangle is 15 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

00:15 Let's use the formula for calculating the area of a parallelogram

00:19 Side(CD) multiplied by height (H)

00:24 Let's substitute the appropriate values and solve for the area

00:37 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 = 32 cm

The height of the rectangle is 15 cm.

Calculate the area of the parallelogram.

Step-by-step solution

To calculate the area of the parallelogram, we'll use the standard area formula for a parallelogram:

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

From the problem, the base $AB = 32 \, \text{cm}$ and the height is $15 \, \text{cm}$ .

Substituting these values into the formula gives:

$\text{Area} = 32 \times 15$

Perform the multiplication:

$32 \times 15 = 480$

Thus, the area of the parallelogram is $\text{480 cm}^2$ .

The correct answer is choice 4: 480.

Final Answer

480

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base multiplied by perpendicular height
Calculation: Use $32 \times 15 = 480$ square centimeters
Verification: Check units are squared and height is perpendicular ✓

Common Mistakes

Avoid these frequent errors

Using slanted side length instead of perpendicular height
Don't measure along the slanted side of the parallelogram as height = wrong area calculation! The slanted side is longer than the perpendicular distance. Always use the perpendicular distance from base to opposite side as height.

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?

Height is the perpendicular distance between parallel sides, while side length is measured along the slanted edge. In this problem, height = 15 cm is the vertical distance, not the slanted side.

Why do we use base × height instead of length × width?

A parallelogram is not a rectangle! Length × width only works for rectangles. For parallelograms, we need base × perpendicular height because the sides are slanted.

How do I identify which measurement is the base?

Any side can be the base! In this problem, AB = 32 cm is given as the base. The height (15 cm) is always perpendicular to whichever side you choose as base.

What units should my answer have?

Area is always measured in square units. Since the measurements are in centimeters, your answer should be in square centimeters or cm².

Can I use any parallelogram side as the base?

Yes! You can use any side as the base, but then you must use the height that's perpendicular to that specific side. The area will be the same regardless of which side you choose.

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