Calculate Parallelogram Area: Base 6 and Height 3

Q: Why can't I use the slanted side instead of the height?

The slanted side is always longer than the perpendicular height. Using it would give you the area of a rectangle that's bigger than your parallelogram! Only the perpendicular height gives the true area.

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

Look for the perpendicular line - it forms a 90° angle with the base. In this problem, AH is marked as the height because it drops straight down from point A to the base DC.

Q: Does it matter which side I choose as the base?

No! You can use any side as the base, but you must use the perpendicular height to that specific base. The area will always be the same.

Q: What if I don't have the height marked in the diagram?

Look for dashed lines or right angle symbols that show perpendicular distances. Sometimes you'll need to use trigonometry to find the height from given angles and side lengths.

Parallelogram Area with Base and Height

ABCD is a parallelogram.

AH is the height.

DC = 6
AH = 3

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

00:00 Calculate the area of the parallelogram

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

00:10 We'll substitute the side that is the height in the parallelogram

00:16 We'll substitute values according to the given data, calculate and solve

00:20 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.

AH is the height.

DC = 6
AH = 3

What is the area of the parallelogram?

Step-by-step solution

To solve this problem, let's apply the formula for the area of a parallelogram:

The given base $DC$ is 6 cm.
The perpendicular height $AH$ from point $A$ to base $DC$ is 3 cm.

The formula for the area of a parallelogram is:

$\text{Area} = \text{base} \times \text{height}$

Substituting the given values, we have:

$\text{Area} = 6 \times 3$

Thus, the area of parallelogram $ABCD$ is:

$\text{Area} = 18 \, \text{cm}^2$

Therefore, the solution to the problem is $18 \, \text{cm}^2$ .

Final Answer

18 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area = base × height for any parallelogram
Technique: Use perpendicular height, not slanted side: 6 × 3 = 18
Check: Height must be perpendicular to base for correct calculation ✓

Common Mistakes

Avoid these frequent errors

Using slanted side length instead of perpendicular height
Don't multiply base by the slanted side AD = wrong area! The slanted side is longer than the height and gives an inflated result. Always use the perpendicular distance (height) from the base to the opposite side.

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 the slanted side instead of the height?

The slanted side is always longer than the perpendicular height. Using it would give you the area of a rectangle that's bigger than your parallelogram! Only the perpendicular height gives the true area.

How do I know which measurement is the height?

Look for the perpendicular line - it forms a 90° angle with the base. In this problem, AH is marked as the height because it drops straight down from point A to the base DC.

Does it matter which side I choose as the base?

No! You can use any side as the base, but you must use the perpendicular height to that specific base. The area will always be the same.

What if I don't have the height marked in the diagram?

Look for dashed lines or right angle symbols that show perpendicular distances. Sometimes you'll need to use trigonometry to find the height from given angles and side lengths.

Is the area formula the same for all parallelograms?

Yes! Whether it's a rectangle, rhombus, or any parallelogram, the formula is always $\text{Area} = \text{base} \times \text{height}$ . Only the perpendicular height matters.

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