Calculate Parallelogram Area Using Exterior Height: 10-Unit Height Problem

Q: What's the difference between exterior and interior height?

Exterior height extends outside the parallelogram, while interior height stays inside. Both are perpendicular to the base, so they give the same measurement and same area result!

Q: How do I know which side to use as the base?

You can choose any side as the base! Just make sure to use the perpendicular height to that specific side. Different base choices give the same area.

Q: What if the height line doesn't touch the parallelogram?

That's normal for exterior height! The height line extends beyond the parallelogram to form a right angle with the base. The perpendicular distance is what matters, not where the line ends.

Q: Can I use the formula base × height for any parallelogram?

Yes! $ \text{Area} = \text{base} \times \text{height} $ works for all parallelograms, including rectangles, rhombuses, and squares. Just remember height must be perpendicular to the base.

Parallelogram Area with Exterior Height

Given the parallelogram in which CF is the exterior height of side BD:

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 We'll use the formula to calculate the area of a parallelogram

00:07 Side(BD) multiplied by the height to side (H)

00:14 The height to side BD is CF

00:20 Opposite sides are equal in a parallelogram

00:31 We'll substitute appropriate values in the formula and solve to find the area

00:44 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

Given the parallelogram in which CF is the exterior height of side BD:

Calculate the area of the parallelogram.

Step-by-step solution

To solve for the area of the parallelogram, consider the following details:

Step 1: Identify the base and height of the parallelogram. Here, the side that is used as the base is BD, which has an external perpendicular line, CF, indicating the height.
Step 2: Given that $CF = 12$ (the height), and the base $BD = 10$ , you can calculate the area using the formula $\text{Area} = \text{base} \times \text{height}$ .

Given these values, the area calculation is as follows:
Step 2: The base $BD$ is 10, and the height $CF$ is 12. Thus:
$\text{Area} = 10 \times 12 = 120$ .

Therefore, the area of the parallelogram is $120$ .

Final Answer

120

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times perpendicular height
Technique: Use BD = 10 as base, CF = 12 as height
Check: Verify height is perpendicular to chosen base side ✓

Common Mistakes

Avoid these frequent errors

Using slanted side length instead of perpendicular height
Don't measure the slanted distance from C to side BD = wrong area calculation! The slanted measurement isn't perpendicular, so it's longer than the true height. Always use the perpendicular distance (exterior height CF) for accurate area calculation.

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 exterior and interior height?

Exterior height extends outside the parallelogram, while interior height stays inside. Both are perpendicular to the base, so they give the same measurement and same area result!

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

Parallelogram sides aren't perpendicular to each other! You need base × perpendicular height, not base × adjacent side. Only rectangles let you multiply any two adjacent sides.

How do I know which side to use as the base?

You can choose any side as the base! Just make sure to use the perpendicular height to that specific side. Different base choices give the same area.

What if the height line doesn't touch the parallelogram?

That's normal for exterior height! The height line extends beyond the parallelogram to form a right angle with the base. The perpendicular distance is what matters, not where the line ends.

Can I use the formula base × height for any parallelogram?

Yes! $\text{Area} = \text{base} \times \text{height}$ works for all parallelograms, including rectangles, rhombuses, and squares. Just remember height must be perpendicular to the base.

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