Parallelogram Area Calculation: Using Perpendicular Heights BE=4 and BF=8

Q: How do I know which height goes with which side?

The height must be perpendicular to the side you're using as the base. In this problem, BE is perpendicular to DE, so use BE = 4 with DC = 12. Similarly, BF is perpendicular to DF, so use BF = 8 with AD = 6.

Q: Why are there two different ways to calculate the same area?

A parallelogram has two pairs of parallel sides, so you can use either pair as base and height. Both methods must give the same result because it's the same shape - this is a great way to check your work!

Q: Can I use the slanted sides instead of the heights?

No! You must use perpendicular heights, not the slanted sides. The area formula requires the perpendicular distance between parallel sides, which is what BE and BF represent.

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

Look for the right angle symbols (small squares) in the diagram. These show where lines meet at 90° angles. The dashed lines BE and BF are the perpendicular heights.

Parallelogram Area with Perpendicular Heights

ABCD parallelogram, it is known that:

BE is perpendicular to DE

BF is perpendicular to DF

BF=8 BE=4 AD=6 DC=12

Calculate the area of the parallelogram in 2 different ways

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find BE

00:05 To find the area of the parallelogram, multiply the height (FB) by side (AD)

00:10 Let's substitute appropriate values and solve for the area

00:16 Now let's use the same area formula to find the second height (BE)

00:20 Let's substitute appropriate values and solve for BE

00:29 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 parallelogram, it is known that:

BE is perpendicular to DE

BF is perpendicular to DF

BF=8 BE=4 AD=6 DC=12

Calculate the area of the parallelogram in 2 different ways

Step-by-step solution

In this exercise, we are given two heights and two sides.

It is important to keep in mind: The external height can also be used to calculate the area

Therefore, we can perform the operation of the following exercise:

The height BF * the side AD

8*6

The height BE the side DC
4*12

The solution of these two exercises is 48, which is the area of the parallelogram.

Final Answer

48 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area = base × height, where height is perpendicular to base
Method: Use BF = 8 with AD = 6, or BE = 4 with DC = 12
Check: Both calculations give 48 cm² confirming the answer ✓

Common Mistakes

Avoid these frequent errors

Pairing wrong height with wrong side
Don't use BF with DC or BE with AD = wrong area calculation! Heights must be perpendicular to their corresponding sides. Always match perpendicular height BF = 8 with side AD = 6, and perpendicular height BE = 4 with side DC = 12.

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 height goes with which side?

The height must be perpendicular to the side you're using as the base. In this problem, BE is perpendicular to DE, so use BE = 4 with DC = 12. Similarly, BF is perpendicular to DF, so use BF = 8 with AD = 6.

Why are there two different ways to calculate the same area?

A parallelogram has two pairs of parallel sides, so you can use either pair as base and height. Both methods must give the same result because it's the same shape - this is a great way to check your work!

What if I get different answers from the two methods?

If your answers don't match, you've made an error! Check that you're using the correct perpendicular height with each side. Remember: $8 \times 6 = 48$ and $4 \times 12 = 48$ .

Can I use the slanted sides instead of the heights?

No! You must use perpendicular heights, not the slanted sides. The area formula requires the perpendicular distance between parallel sides, which is what BE and BF represent.

How do I identify perpendicular heights in the diagram?

Look for the right angle symbols (small squares) in the diagram. These show where lines meet at 90° angles. The dashed lines BE and BF are the perpendicular heights.

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