Calculate Parallelogram Area: 10cm Base and 5cm Height Problem

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

The height of a parallelogram is always the perpendicular distance between the parallel sides, not the slanted side length. Using the slanted side gives you a larger number and the wrong area!

Q: Is this the same formula as for rectangles?

Yes! The formula $ A = \text{base} \times \text{height} $ works for both rectangles and parallelograms. The key is using the perpendicular height, not the side length.

Q: How do I know which side is the base?

You can choose any side as the base! Just make sure you use the height that's perpendicular to that base. The area will be the same regardless of which side you pick.

Q: What if the height isn't drawn in the diagram?

Look for a dashed line or a line marked with a right angle symbol (⊥). The height is always shown as perpendicular to the base, often as a vertical line when the base is horizontal.

Q: Why is my answer 50 cm² and not just 50?

When you multiply length × length, the units multiply too! $ 10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2 $. The cm² tells us we're measuring area, not just length.

Parallelogram Area with Base and Height

AB = 10 cm

The height of the rectangle is 5 cm.

Calculate the area of the parallelogram.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

00:18 Let's use the formula for calculating the area of a parallelogram

00:23 Side(CD) multiplied by height (H)

00:27 Let's substitute appropriate values and solve for the area

00:35 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 = 10 cm

The height of the rectangle is 5 cm.

Calculate the area of the parallelogram.

Step-by-step solution

To solve this problem, we'll apply the formula for the area of a parallelogram:

Step 1: Identify the base and the height from the given information.
Step 2: Use the formula for the area of a parallelogram: $A = \text{base} \times \text{height}$ .
Step 3: Calculate the area using the given values.

Let's proceed with the solution:
Step 1: The given base $AB$ is 10 cm, and the height is 5 cm.
Step 2: The formula for the area of a parallelogram is $A = \text{base} \times \text{height}$ .
Step 3: Substituting the provided values, we get:
$A = 10 \, \text{cm} \times 5 \, \text{cm}$
$A = 50 \, \text{cm}^2$

Therefore, the area of the parallelogram is $50 \, \text{cm}^2$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times height for parallelograms
Technique: Use perpendicular height, not slanted side length (5 cm)
Check: Units become cm² when multiplying cm × cm ✓

Common Mistakes

Avoid these frequent errors

Using slanted side instead of perpendicular height
Don't measure the slanted side of the parallelogram and call it height = wrong area! The slanted side is longer than the perpendicular distance. Always use the perpendicular height (the shortest distance between parallel sides).

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

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

The height of a parallelogram is always the perpendicular distance between the parallel sides, not the slanted side length. Using the slanted side gives you a larger number and the wrong area!

Is this the same formula as for rectangles?

Yes! The formula $A = \text{base} \times \text{height}$ works for both rectangles and parallelograms. The key is using the perpendicular height, not the side length.

How do I know which side is the base?

You can choose any side as the base! Just make sure you use the height that's perpendicular to that base. The area will be the same regardless of which side you pick.

What if the height isn't drawn in the diagram?

Look for a dashed line or a line marked with a right angle symbol (⊥). The height is always shown as perpendicular to the base, often as a vertical line when the base is horizontal.

Why is my answer 50 cm² and not just 50?

When you multiply length × length, the units multiply too! $10 \text{ cm} \times 5 \text{ cm} = 50 \text{ cm}^2$ . The cm² tells us we're measuring area, not just length.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime