Parallelogram Area 4x with Height 2: Finding Side Length AD

Q: How do I know which side is the base and which is the height?

The height is always the perpendicular distance between parallel sides. In this problem, AE is labeled as the height with a right angle symbol. The base can be any side the height is drawn to.

Q: Why is the answer in terms of x instead of a number?

Since the area is given as $ 4x $ (an algebraic expression), the base must also be in terms of x. We're finding the relationship between the base and the variable x, not solving for x itself.

Q: Can I use a different side as the base?

Yes! You could use any side as the base, but you'd need the perpendicular height to that side. Since we're given AE = 2 as the height to side CD (or AB), using AD as the base gives us the simplest calculation.

Q: How do I check if AD = 2x is correct?

Substitute back into the area formula: Area = Base × Height = 2x × 2 = 4x. This matches the given area, so our answer is correct!

Q: What if I accidentally used the wrong formula?

If you used triangle area formula $ \frac{1}{2} \times base \times height $, you'd get AD = 4x instead. Always remember parallelograms don't have the $ \frac{1}{2} $ factor!

Parallelogram Area with Algebraic Expressions

Look at the parallelogram ABCD.

The area of ABCD is $4x$ .

$AE$ is the height of the parallelogram.

$AE=2$

Calculate AD.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AD

00:03 We'll use the formula for calculating the area of a parallelogram (base times height)

00:12 We'll substitute appropriate values according to the given data, and express BC

00:39 Opposite sides are equal in a parallelogram

00:49 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

Look at the parallelogram ABCD.

The area of ABCD is $4x$ .

$AE$ is the height of the parallelogram.

$AE=2$

Calculate AD.

Step-by-step solution

To solve this problem, let's analyze and calculate step by step:

The formula for the area of a parallelogram is given by:

$\text{Area} = \text{Base} \times \text{Height}$

We're given:

The area is $4x$ .
The height $AE = 2$ .

We need to find the base $AD$ . Let's plug these values into the formula:

$4x = AD \times 2$

Now, solve for $AD$ by dividing both sides by 2:

$AD = \frac{4x}{2} = 2x$

Therefore, the length of $AD$ is $2x$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = Base × Height for parallelograms
Technique: Substitute known values: $4x = AD \times 2$
Check: Verify by calculating area with AD = 2x: 2x × 2 = 4x ✓

Common Mistakes

Avoid these frequent errors

Confusing base and height in area formula
Don't use AD as height when AE is given as height = wrong calculation! This mixes up the perpendicular height with a side length, leading to incorrect equations. Always identify which measurement is the perpendicular height before applying the area formula.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the parallelogram according to the data in the diagram.

FAQ

Everything you need to know about this question

How do I know which side is the base and which is the height?

The height is always the perpendicular distance between parallel sides. In this problem, AE is labeled as the height with a right angle symbol. The base can be any side the height is drawn to.

Why is the answer in terms of x instead of a number?

Since the area is given as $4x$ (an algebraic expression), the base must also be in terms of x. We're finding the relationship between the base and the variable x, not solving for x itself.

Can I use a different side as the base?

Yes! You could use any side as the base, but you'd need the perpendicular height to that side. Since we're given AE = 2 as the height to side CD (or AB), using AD as the base gives us the simplest calculation.

How do I check if AD = 2x is correct?

Substitute back into the area formula: Area = Base × Height = 2x × 2 = 4x. This matches the given area, so our answer is correct!

What if I accidentally used the wrong formula?

If you used triangle area formula $\frac{1}{2} \times base \times height$ , you'd get AD = 4x instead. Always remember parallelograms don't have the $\frac{1}{2}$ factor!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime