Calculate Parallelogram Area: 38cm Perimeter with Proportional Sides

Q: What does 'three times shorter' actually mean?

If CE = x, then 'three times shorter' means $ AD = \frac{x}{3} $. Think of it as: AD is one-third the length of CE. Don't confuse this with 'three times longer' which would be 3x!

Q: Why do we use the perimeter formula 2(AB + AD)?

In a parallelogram, opposite sides are equal. So we have two sides of length AB and two sides of length AD. The total perimeter is $ 2 \times AB + 2 \times AD = 2(AB + AD) $.

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

For area calculation, you can use any side as the base as long as you use the perpendicular height to that side. Here, CE is perpendicular to AD, so we use AD as base and CE as height.

Q: What if I get a different value for x?

Double-check your algebra! The equation should be $ 38 = 2(2x + \frac{x}{3}) $. Multiply out carefully: $ 38 = 4x + \frac{2x}{3} = \frac{12x + 2x}{3} = \frac{14x}{3} $, so $ x = \frac{38 \times 3}{14} = \frac{114}{14} \approx 8.14 $.

Parallelogram Area with Proportional Side Relationships

ABCD is a parallelogram with a perimeter of 38 cm.

AB is twice as long as CE.

AD is three times shorter than CE.

CE is the height of the parallelogram.

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 Let's mark the height with X

00:07 Side lengths according to the given data, we'll express the sides using X

00:19 The perimeter of the parallelogram equals the sum of its sides

00:29 Opposite sides are equal in a parallelogram

00:34 We'll substitute appropriate values and solve for X

00:49 Pay attention to proper parentheses

00:56 Isolate X

01:02 And this is the height X

01:10 Now let's substitute X value to find side AD

01:14 Now we can calculate the parallelogram's area

01:19 Multiply height(EC) by side(AD)

01:23 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 is a parallelogram with a perimeter of 38 cm.

AB is twice as long as CE.

AD is three times shorter than CE.

CE is the height of the parallelogram.

Calculate the area of the parallelogram.

Step-by-step solution

Let's call CE as X

According to the data

$AB=x+2,AD=x-3$

The perimeter of the parallelogram:

$2(AB+AD)$

$38=2(x+2+x-3)$

$38=2(2x-1)$

$38=4x-2$

$38+2=4x$

$40=4x$

$x=10$

Now it can be argued:

$AD=10-3=7,CE=10$

The area of the parallelogram:

$CE\times AD=10\times7=70$

Final Answer

70 cm²

Key Points to Remember

Essential concepts to master this topic

Setup: Use variables to express proportional relationships between sides
Technique: Set CE = x, then AB = 2x and AD = x/3
Check: Verify perimeter: 2(2x + x/3) = 38 gives x = 10 ✓

Common Mistakes

Avoid these frequent errors

Confusing the proportional relationships
Don't mix up 'twice as long' and 'three times shorter' = wrong side lengths! Students often write AD = 3x instead of AD = x/3. Always read carefully: 'three times shorter' means divide by 3, not multiply by 3.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the parallelogram ABCD, given that CD is parallel to AB.

FAQ

Everything you need to know about this question

What does 'three times shorter' actually mean?

If CE = x, then 'three times shorter' means $AD = \frac{x}{3}$ . Think of it as: AD is one-third the length of CE. Don't confuse this with 'three times longer' which would be 3x!

Why do we use the perimeter formula 2(AB + AD)?

In a parallelogram, opposite sides are equal. So we have two sides of length AB and two sides of length AD. The total perimeter is $2 \times AB + 2 \times AD = 2(AB + AD)$ .

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

For area calculation, you can use any side as the base as long as you use the perpendicular height to that side. Here, CE is perpendicular to AD, so we use AD as base and CE as height.

What if I get a different value for x?

Double-check your algebra! The equation should be $38 = 2(2x + \frac{x}{3})$ . Multiply out carefully: $38 = 4x + \frac{2x}{3} = \frac{12x + 2x}{3} = \frac{14x}{3}$ , so $x = \frac{38 \times 3}{14} = \frac{114}{14} \approx 8.14$ .

Can I solve this problem without using variables?

Variables make this much easier! Without them, you'd have to guess and check different values. Using x for CE lets you write clear equations and solve systematically.

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Calculate Parallelogram Area: 38cm Perimeter with Proportional Sides

Parallelogram Area with Proportional Side Relationships

❤️ 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

What does 'three times shorter' actually mean?

Why do we use the perimeter formula 2(AB + AD)?

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

What if I get a different value for x?

Can I solve this problem without using variables?

🌟 Unlock Your Math Potential

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