Calculate Parallelogram Area: 10 Units Base with 6 Units Height

Q: Why can't I use the slanted side that's labeled 8?

The slanted side (8 cm) is longer than the actual height! Think of it like measuring a ladder against a wall - the ladder is longer than the wall's height. Always use the perpendicular distance between the parallel sides.

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

Look for the dashed line that forms a 90° angle with the base! In this diagram, the green dashed line showing 6 cm is perpendicular to the base, making it the true height.

Q: Does it matter which side I call the base?

No! You can use any side as the base, but then you must use the perpendicular height to that specific base. The area will be the same either way.

Q: Why is my answer different from my friend's?

Check if you both used the perpendicular height (6 cm) instead of the slanted side (8 cm). This is the most common mistake! The correct answer is $ 10 \times 6 = 60 \text{ cm}^2 $.

Parallelogram Area with Perpendicular Height

Calculate the area of the following 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

00:04 We'll use the formula for calculating the area of a parallelogram (height times side)

00:15 We'll substitute the side that is the height in the parallelogram

00:21 We'll substitute values according to the given data, calculate and solve

00:25 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

Calculate the area of the following parallelogram:

Step-by-step solution

To calculate the area of the parallelogram, we will simply apply the formula for the area of a parallelogram:

Identify the base: The length of the base is $10 \, \text{cm}$ .
Identify the height: The perpendicular height is given as $6 \, \text{cm}$ .

Apply the formula: $\text{Area} = \text{base} \times \text{height}$ .

Substitute the known values: $\text{Area} = 10 \, \text{cm} \times 6 \, \text{cm}$ .

Calculate the result: $\text{Area} = 60 \, \text{cm}^2$ .

Therefore, the area of the parallelogram is $60 \, \text{cm}^2$ .

Final Answer

60 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times perpendicular height only
Technique: Base = 10 cm, height = 6 cm, so Area = 60 cm²
Check: Height is perpendicular (dashed line), not slanted side = correct ✓

Common Mistakes

Avoid these frequent errors

Using slanted side instead of perpendicular height
Don't multiply base by the slanted side (8 cm) = 80 cm²! The slanted side is longer than the perpendicular distance between parallel sides. Always use the perpendicular height (the dashed line showing 6 cm).

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 that's labeled 8?

The slanted side (8 cm) is longer than the actual height! Think of it like measuring a ladder against a wall - the ladder is longer than the wall's height. Always use the perpendicular distance between the parallel sides.

How do I know which measurement is the height?

Look for the dashed line that forms a 90° angle with the base! In this diagram, the green dashed line showing 6 cm is perpendicular to the base, making it the true height.

What if I don't see a dashed line showing height?

Sometimes the height isn't drawn! Look for a measurement that's shorter than the slanted sides - that's usually the perpendicular height. The height is always the shortest distance between parallel sides.

Does it matter which side I call the base?

No! You can use any side as the base, but then you must use the perpendicular height to that specific base. The area will be the same either way.

Why is my answer different from my friend's?

Check if you both used the perpendicular height (6 cm) instead of the slanted side (8 cm). This is the most common mistake! The correct answer is $10 \times 6 = 60 \text{ cm}^2$ .

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