Calculate Parallelogram Area: 90° Right Angle with 9 and 11 Unit Measurements

Q: Why can't I use side AD as the height?

Side AD is a slanted side, not the perpendicular height! Height must be the shortest distance between parallel sides. Since angle AEC = 90°, AE is perpendicular to base CD.

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

The base can be any side of the parallelogram. The height is always perpendicular to that base. Here, CD = 11 is the base, and AE = 9 is the perpendicular height.

Q: What does the 90° angle tell me?

The 90° angle at point E means that line AE is perpendicular to the base. This confirms that AE = 9 is the correct height to use in the area formula.

Q: Is this different from finding the area of a rectangle?

No! The formula is identical: Area = base × height. The key is that height must always be perpendicular to the base, whether it's a rectangle or parallelogram.

Parallelogram Area with Perpendicular Height

Below is the parallelogram ABCD.

AEC = 90°

What is the area of the parallelogram?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:10 Let's find the area of the parallelogram.

00:13 To do this, multiply the height, A E, with the base, D C.

00:24 Now, plug in the values you have and solve for the area.

00:32 And that's how we find the solution to our question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is the parallelogram ABCD.

AEC = 90°

What is the area of the parallelogram?

Step-by-step solution

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

Step 1: Identify the base and height from the given diagram.
Step 2: Apply the area formula for the parallelogram.
Step 3: Calculate the area using the identified base and height.

Let's execute these steps:

Step 1: In parallelogram ABCD, the length of side CD is given as 11 cm. Since angle AEC is a right angle, AE, which measures 9 cm, serves as the height of the parallelogram.

Step 2: Use the formula for the area of a parallelogram:
$\text{Area} = \text{base} \times \text{height}$

Step 3: Substitute the values into the formula:
$\text{Area} = 11 \, \text{cm} \times 9 \, \text{cm} = 99 \, \text{cm}^2$

Thus, the area of the parallelogram ABCD is $\mathbf{99 \, \text{cm}^2}$ .

Final Answer

$99$ cm².

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times perpendicular height
Technique: Use AE = 9 as height, CD = 11 as base: $11 \times 9 = 99$
Check: Height must be perpendicular to base (AEC = 90°) ✓

Common Mistakes

Avoid these frequent errors

Using the slanted side as height
Don't use side AD (the slant) as height = wrong area calculation! The slanted side is longer than the perpendicular height, giving an area that's too large. Always use the perpendicular distance between parallel sides as 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 can't I use side AD as the height?

Side AD is a slanted side, not the perpendicular height! Height must be the shortest distance between parallel sides. Since angle AEC = 90°, AE is perpendicular to base CD.

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

The base can be any side of the parallelogram. The height is always perpendicular to that base. Here, CD = 11 is the base, and AE = 9 is the perpendicular height.

What does the 90° angle tell me?

The 90° angle at point E means that line AE is perpendicular to the base. This confirms that AE = 9 is the correct height to use in the area formula.

Could I use a different base and height?

Yes! You could use AB as the base, but then you'd need to find the perpendicular distance from AB to CD. The area will always be the same regardless of which base you choose.

Is this different from finding the area of a rectangle?

No! The formula is identical: Area = base × height. The key is that height must always be perpendicular to the base, whether it's a rectangle or parallelogram.

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Calculate Parallelogram Area: 90° Right Angle with 9 and 11 Unit Measurements

Parallelogram Area with Perpendicular Height

❤️ 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 can't I use side AD as the height?

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

What does the 90° angle tell me?

Could I use a different base and height?

Is this different from finding the area of a rectangle?

🌟 Unlock Your Math Potential

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