Calculate Length DF in Parallelogram ABCD: Given AB=12cm, ED=8cm, BC=10cm

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

The height must be perpendicular to its base. In this diagram, ED is perpendicular to AB, and DF is perpendicular to BC. Look for the right angle symbols to identify correct pairs!

Q: Why can I calculate the same area two different ways?

A parallelogram has a fixed area regardless of which base you choose! This property lets us set up the equation: $ \text{base}_1 \times \text{height}_1 = \text{base}_2 \times \text{height}_2 $

Q: What if I get a decimal answer?

Decimal answers are completely normal in geometry! $ 9.6 $ cm is exact and correct. Always check your division: $ \frac{96}{10} = 9.6 $

Q: Can I use any two sides as bases?

Yes! In a parallelogram, you can use any side as a base, but you must use the height that's perpendicular to that specific base. Each base has its own corresponding height.

Q: How do I verify my answer is correct?

Substitute back: $ BC \times DF = 10 \times 9.6 = 96 $ square cm. This should equal $ AB \times ED = 12 \times 8 = 96 $ square cm. Same area = correct answer!

Parallelogram Area with Multiple Heights

Look at the parallelogram ABCD.

AB = 12 cm

ED = 8 cm

BC = 10 cm

Calculate the length of DF.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find DF

00:04 We'll use the formula to calculate the area of a parallelogram

00:07 Side(AB) multiplied by height (DE)

00:11 We'll substitute appropriate values and solve to find the area

00:20 This is the area of the parallelogram

00:23 Now we want to calculate the area using the second height

00:27 We'll use the formula again to calculate the area with height DF

00:30 We'll substitute appropriate values and solve to find DF

00:53 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

Look at the parallelogram ABCD.

AB = 12 cm

ED = 8 cm

BC = 10 cm

Calculate the length of DF.

Step-by-step solution

To solve for the length of $DF$ , let's consider both ways of calculating the area of parallelogram $ABCD$ :

Step 1: Calculate area using base $AB$ :
$\text{Area} = AB \times ED = 12 \times 8 = 96$ square cm.
Step 2: Calculate area using base $BC$ :
$\text{Area} = BC \times DF = 10 \times DF$ .
Equate 96 to $10 \times DF$ :
$10 \times DF = 96$ .
Step 3: Solve for $DF$ by dividing by 10:
$DF = \frac{96}{10} = 9.6$ cm.

Therefore, the length of $DF$ is $9.6$ cm.

Hence, the correct answer is choice 4, which is $9.6$ cm.

Final Answer

$9.6$ cm

Key Points to Remember

Essential concepts to master this topic

Area Formula: Parallelogram area equals base times corresponding height
Technique: Set $AB \times ED = BC \times DF$ to find unknown height
Check: Verify $12 \times 8 = 10 \times 9.6 = 96$ square cm ✓

Common Mistakes

Avoid these frequent errors

Using incorrect base-height pairs
Don't pair AB with DF or BC with ED = wrong calculation! Heights must be perpendicular to their corresponding bases. Always match each base with its perpendicular height: AB goes with ED, and BC goes with DF.

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 base?

The height must be perpendicular to its base. In this diagram, ED is perpendicular to AB, and DF is perpendicular to BC. Look for the right angle symbols to identify correct pairs!

Why can I calculate the same area two different ways?

A parallelogram has a fixed area regardless of which base you choose! This property lets us set up the equation: $\text{base}_1 \times \text{height}_1 = \text{base}_2 \times \text{height}_2$

What if I get a decimal answer?

Decimal answers are completely normal in geometry! $9.6$ cm is exact and correct. Always check your division: $\frac{96}{10} = 9.6$

Can I use any two sides as bases?

Yes! In a parallelogram, you can use any side as a base, but you must use the height that's perpendicular to that specific base. Each base has its own corresponding height.

How do I verify my answer is correct?

Substitute back: $BC \times DF = 10 \times 9.6 = 96$ square cm. This should equal $AB \times ED = 12 \times 8 = 96$ square cm. Same area = correct answer!

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Calculate Length DF in Parallelogram ABCD: Given AB=12cm, ED=8cm, BC=10cm

Parallelogram Area with Multiple Heights

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which height goes with which base?

Why can I calculate the same area two different ways?

What if I get a decimal answer?

Can I use any two sides as bases?

How do I verify my answer is correct?

🌟 Unlock Your Math Potential

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