Calculate Parallelogram Area: Finding Area with line 7 and side 5

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

The height is always the perpendicular distance between the parallel sides. Look for the line that forms a 90° angle with the base - that's your height!

Q: Can I use any side as the base?

Yes! You can choose either pair of parallel sides as your base. Just make sure to use the perpendicular height to that chosen base.

Q: What's the difference between a parallelogram and rectangle area?

The formula is exactly the same: $ \text{Area} = \text{base} \times \text{height} $. A rectangle is just a special parallelogram where all angles are 90°!

Q: Why isn't the area 7 times the slanted side?

Because the slanted side is not perpendicular to the base! Area measures the space inside the shape, which depends on the perpendicular height, not the diagonal distance.

Q: How do I find the height if it's not directly given?

Look for right angle markers in the diagram, or use trigonometry if you know an angle. The height is always the shortest distance between the parallel sides.

Parallelogram Area with Base and Height

Calculate the area of the parallelogram using the data in the figure:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of the parallelogram

00:03 We will use the formula to calculate the area of a parallelogram (base times height)

00:06 We will substitute appropriate values and solve to find the area

00:09 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

Calculate the area of the parallelogram using the data in the figure:

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 provides us with a base ( $b$ ) of 7 units and a height ( $h$ ) of 5 units, perpendicular to this base.
Step 2: We'll apply the formula for the area of a parallelogram, which is $\text{Area} = b \times h$ .
Step 3: Substituting the given values, $\text{Area} = 7 \times 5 = 35$ .

Therefore, the area of the parallelogram is $35$ square units.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times perpendicular height
Technique: Identify height as perpendicular distance: 5 units to base
Check: Verify dimensions are perpendicular: 7 × 5 = 35 square units ✓

Common Mistakes

Avoid these frequent errors

Using the slanted side length instead of perpendicular height
Don't use the diagonal slanted side as height = wrong area calculation! The slanted side is longer than the perpendicular height and gives 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

How do I know which measurement is the height?

The height is always the perpendicular distance between the parallel sides. Look for the line that forms a 90° angle with the base - that's your height!

Can I use any side as the base?

Yes! You can choose either pair of parallel sides as your base. Just make sure to use the perpendicular height to that chosen base.

What's the difference between a parallelogram and rectangle area?

The formula is exactly the same: $\text{Area} = \text{base} \times \text{height}$ . A rectangle is just a special parallelogram where all angles are 90°!

Why isn't the area 7 times the slanted side?

Because the slanted side is not perpendicular to the base! Area measures the space inside the shape, which depends on the perpendicular height, not the diagonal distance.

How do I find the height if it's not directly given?

Look for right angle markers in the diagram, or use trigonometry if you know an angle. The height is always the shortest distance between the parallel sides.

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