Calculate Parallelogram Area: 15 cm Base × 6 cm Height

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

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

Q: Why can't I just multiply any two sides together?

Because parallelograms are slanted! You need the perpendicular height to get the true area. Multiplying two sides gives you something bigger than the actual area.

Q: How do I identify the base and height from a diagram?

The base can be any side you choose. The height is always drawn with a right angle symbol showing it's perpendicular to the base.

Q: What if the parallelogram is tilted differently?

No problem! The area formula $ A = b \times h $ works for any orientation. Just make sure your height is always perpendicular to your chosen base.

Q: Do I need to include units in my final answer?

Yes! Always include square units (like cm², m², etc.) for area. Since we're multiplying length × length, the result is always squared units.

Parallelogram Area with Base and Height

AB = 15 cm

The height of the rectangle is 6 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

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

00:26 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 = 15 cm

The height of the rectangle is 6 cm.

Calculate the area of the parallelogram.

Step-by-step solution

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

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

Now, let's work through each step:
Step 1: The base $b$ is equal to the length $AB$ , which is $\text{15 cm}$ . The height $h$ corresponding to this base is $\text{6 cm}$ .
Step 2: We'll use the formula for the area of a parallelogram:
$\text{Area} = b \times h$ .
Step 3: Plugging in our values, we have:
$\text{Area} = 15 \times 6 = 90 \, \text{cm}^2$ .

Therefore, the solution to the problem is $\text{Area} = 90 \, \text{cm}^2$ , which matches choice .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times height (A = b × h)
Technique: Use perpendicular height, not slanted side: 15 × 6 = 90
Check: Verify units are squared and calculation matches formula ✓

Common Mistakes

Avoid these frequent errors

Using slanted side length instead of perpendicular height
Don't use the slanted side length as height = wrong area calculation! The slanted side is longer than the perpendicular height, giving an overestimate. Always use the perpendicular distance between parallel sides 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 in a parallelogram?

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

Why can't I just multiply any two sides together?

Because parallelograms are slanted! You need the perpendicular height to get the true area. Multiplying two sides gives you something bigger than the actual area.

How do I identify the base and height from a diagram?

The base can be any side you choose. The height is always drawn with a right angle symbol showing it's perpendicular to the base.

What if the parallelogram is tilted differently?

No problem! The area formula $A = b \times h$ works for any orientation. Just make sure your height is always perpendicular to your chosen base.

Do I need to include units in my final answer?

Yes! Always include square units (like cm², m², etc.) for area. Since we're multiplying length × length, the result is always squared units.

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