Calculate Parallelogram Area Using 4:7 Ratio: Height = 8 Units

Q: Why is AE the height and not a side of the parallelogram?

Point E lies directly below point A, creating a perpendicular line to the base DC. This makes AE the height (perpendicular distance), not a side of the parallelogram.

Q: How do I use the ratio 4:7 to find the actual lengths?

Set up the ratio as $ AE:DC = 4x:7x $. Since AE = 8, solve $ 4x = 8 $ to get $ x = 2 $. Then $ DC = 7 \times 2 = 14 $.

Q: Can I use any side as the base for a parallelogram?

Yes! You can use any side as the base, but you must use the perpendicular height to that base. Different base choices give the same area.

Q: What if the ratio was given as 7:4 instead?

The calculation method stays the same! Set $ AE = 7x $ and $ DC = 4x $, then solve $ 7x = 8 $ to find x and calculate DC.

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

Look for the perpendicular distance between parallel sides. In this diagram, AE forms a right angle with the base, shown by the small square symbol at point E.

Parallelogram Area with Proportional Segments

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

Calculate the area of the parallelogram ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's find the area of the parallelogram.

00:17 Check the ratio of height to side, using the given data.

00:25 Multiply by DC, to get rid of the fraction.

00:32 Next, multiply by the reciprocal, again to eliminate the fraction.

00:46 Now, set the value for AE using the given data.

00:59 This tells us the size of DC.

01:02 We'll use the formula to find the parallelogram's area.

01:06 Multiply side, DC, by height, AE.

01:10 Plug in the right values, and solve to get the area.

01:14 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Shown below is the parallelogram ABCD.

The ratio between AE and DC is 4:7.

Calculate the area of the parallelogram ABCD.

Step-by-step solution

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

Step 1: Assume $AE = 4x$ and $DC = 7x$ . The ratio between AE and DC is given as 4:7.
Step 2: Given $AE = 8$ cm, we can write: $4x = 8$ . Solve for x: $x = 2$ cm.
Step 3: Substitute $x = 2$ into $DC = 7x$ to find DC: $\text{DC} = 7 \times 2 = 14$ cm.
Step 4: The area of the parallelogram is given by base $\times$ height. Here, base $DC = 14$ cm and height $AE = 8$ cm, so the area is: $\text{Area} = 14 \times 8 = 112 \text{ cm}^2.$

Thus, the area of the parallelogram ABCD is $112$ cm².

Final Answer

$112$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times height
Technique: Use ratio 4:7 to find DC = 14 when AE = 8
Check: Verify perpendicular height AE creates right angle with base DC ✓

Common Mistakes

Avoid these frequent errors

Using the wrong side as the base
Don't use AE as the base = Area of 8 × 14 = 112, but incorrectly labeled! AE is the perpendicular height, not a side of the parallelogram. Always use DC (the actual side) as the base and AE as the perpendicular 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 is AE the height and not a side of the parallelogram?

Point E lies directly below point A, creating a perpendicular line to the base DC. This makes AE the height (perpendicular distance), not a side of the parallelogram.

How do I use the ratio 4:7 to find the actual lengths?

Set up the ratio as $AE:DC = 4x:7x$ . Since AE = 8, solve $4x = 8$ to get $x = 2$ . Then $DC = 7 \times 2 = 14$ .

Can I use any side as the base for a parallelogram?

Yes! You can use any side as the base, but you must use the perpendicular height to that base. Different base choices give the same area.

What if the ratio was given as 7:4 instead?

The calculation method stays the same! Set $AE = 7x$ and $DC = 4x$ , then solve $7x = 8$ to find x and calculate DC.

How do I know which measurement is the height?

Look for the perpendicular distance between parallel sides. In this diagram, AE forms a right angle with the base, shown by the small square symbol at point E.

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Calculate Parallelogram Area Using 4:7 Ratio: Height = 8 Units

Parallelogram Area with Proportional Segments

❤️ 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

Why is AE the height and not a side of the parallelogram?

How do I use the ratio 4:7 to find the actual lengths?

Can I use any side as the base for a parallelogram?

What if the ratio was given as 7:4 instead?

How do I know which measurement is the height?

🌟 Unlock Your Math Potential

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