Calculate Parallelogram Area: 7cm Base × 2cm Height

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

The height must be perpendicular to the base! Using a slanted side gives you a longer measurement, which makes your area calculation too large. Think of it like measuring the shortest distance between the parallel sides.

Q: How do I identify the perpendicular height in the diagram?

Look for the dashed line that forms a 90° angle with the base. In this problem, AH is drawn as a vertical dashed line, showing it's perpendicular to the horizontal base AB.

Q: What if the parallelogram is tilted differently?

The formula $ \text{Area} = \text{base} \times \text{height} $ works for any parallelogram orientation! Just make sure your height is always perpendicular to whichever side you choose as the base.

Q: Can I use a different side as the base?

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

Q: How is this different from a rectangle's area?

It's exactly the same formula! A rectangle is just a special parallelogram where all angles are 90°. For any parallelogram, you still need base × perpendicular height.

Parallelogram Area with Perpendicular Height

ABCD is a parallelogram.

AH is its height.

Given in cm:

AB = 7

AH = 2

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 the parallelogram

00:03 Opposite sides are equal in a parallelogram

00:12 The formula for calculating parallelogram area is height(AH) times side(DC)

00:22 Let's substitute appropriate values and solve for the area

00:30 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABCD is a parallelogram.

AH is its height.

Given in cm:

AB = 7

AH = 2

Calculate the area of the parallelogram.

Step-by-step solution

To find the area of the parallelogram, we follow these steps:

Step 1: Identify the base and height.
Here, the base $AB$ is $7 \, \text{cm}$ and the perpendicular height $AH$ is $2 \, \text{cm}$ .
Step 2: Use the area formula for a parallelogram:
$\text{Area} = \text{base} \times \text{height}$
Step 3: Substitute the given values into the formula:
$\text{Area} = 7 \times 2 = 14 \, \text{cm}^2$

Therefore, the area of the parallelogram is $\textbf{14 cm}^2$ .

Final Answer

14 cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times perpendicular height only
Technique: Use given measurements: 7 × 2 = 14 cm²
Check: Verify height is perpendicular to base, not slanted side ✓

Common Mistakes

Avoid these frequent errors

Using slanted side length instead of perpendicular height
Don't multiply base by a slanted side = wrong area calculation! The slanted sides are longer than the perpendicular height, giving an inflated area. Always use the perpendicular distance between parallel sides as your 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

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

The height must be perpendicular to the base! Using a slanted side gives you a longer measurement, which makes your area calculation too large. Think of it like measuring the shortest distance between the parallel sides.

How do I identify the perpendicular height in the diagram?

Look for the dashed line that forms a 90° angle with the base. In this problem, AH is drawn as a vertical dashed line, showing it's perpendicular to the horizontal base AB.

What if the parallelogram is tilted differently?

The formula $\text{Area} = \text{base} \times \text{height}$ works for any parallelogram orientation! Just make sure your height is always perpendicular to whichever side you choose as the base.

Can I use a different side as the base?

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

How is this different from a rectangle's area?

It's exactly the same formula! A rectangle is just a special parallelogram where all angles are 90°. For any parallelogram, you still need base × perpendicular height.

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