Calculate Parallelogram Area: Finding Height X with Base 20 and Side 11

Q: Why can't I use DA = 11 as the height?

Height must be perpendicular to the base! DA = 11 is a side length, not the perpendicular distance. The height AE = x is the vertical distance from A to the base CD.

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

You can choose any side as the base! In this problem, we use AB = 20 as the base, so the height is the perpendicular distance to the opposite side CD.

Q: What does the variable x represent exactly?

The variable x represents the height of the parallelogram - the perpendicular distance from point A to the base line CD. This is shown as segment AE in the diagram.

Q: Could the area be 11x instead of 20x?

No! If you used DA = 11 as the base, you'd need a different perpendicular height (not x). Since we're given AE = x as height, we must use the side it's perpendicular to: AB = 20.

Q: Why is my answer 20x and not just a number?

Because the height is given as a variable x! The area formula gives us $ 20 \times x = 20x $. We can't simplify further without knowing the actual value of x.

Area Formula with Variable Height

Calculate the area of the parallelogram ABCD according to the following data:

$DA=11$

$AB=20$

$AE=x$

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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 Opposite sides are equal in a parallelogram

00:06 We'll use the formula for calculating the area of a parallelogram (base times height)

00:11 We'll substitute the appropriate values according to the given data and solve for the area

00:13 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

Calculate the area of the parallelogram ABCD according to the following data:

$DA=11$

$AB=20$

$AE=x$

Step-by-step solution

To find the area of the parallelogram ABCD, we use the following information and process:

Step 1: Recognize that $AB$ , which equals 20 units, is the base of the parallelogram.
Step 2: The height corresponding to this base is the line segment from $A$ perpendicular to $CD$ , denoted $AE = x$ .
Step 3: Use the formula for the area of a parallelogram: $\text{Area} = \text{base} \times \text{height}$ .

Given:

Base $AB = 20$ .
Height $AE = x$ .

Now, applying the formula:

$\text{Area} = AB \times AE = 20 \times x = 20x$

Therefore, the area of the parallelogram ABCD is $20x$ .

The correct answer is $\boxed{20x}$ .

Final Answer

20X

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times height
Technique: Use AB = 20 as base, AE = x as height: 20 × x
Check: Height must be perpendicular to base for correct area calculation ✓

Common Mistakes

Avoid these frequent errors

Using the side length DA = 11 instead of the perpendicular height
Don't use DA = 11 as the height = 11 × 20 = 220x instead of 20x! Side lengths are not heights unless they're perpendicular to the base. Always use the perpendicular distance from base to opposite side as height.

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

Why can't I use DA = 11 as the height?

Height must be perpendicular to the base! DA = 11 is a side length, not the perpendicular distance. The height AE = x is the vertical distance from A to the base CD.

How do I know which side is the base?

You can choose any side as the base! In this problem, we use AB = 20 as the base, so the height is the perpendicular distance to the opposite side CD.

What does the variable x represent exactly?

The variable x represents the height of the parallelogram - the perpendicular distance from point A to the base line CD. This is shown as segment AE in the diagram.

Could the area be 11x instead of 20x?

No! If you used DA = 11 as the base, you'd need a different perpendicular height (not x). Since we're given AE = x as height, we must use the side it's perpendicular to: AB = 20.

Why is my answer 20x and not just a number?

Because the height is given as a variable x! The area formula gives us $20 \times x = 20x$ . We can't simplify further without knowing the actual value of x.

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