Calculate Parallelogram Area: Using 3cm Base and 6cm External Height

Q: What does 'external height' mean in this problem?

An external height is drawn outside the parallelogram, perpendicular to the base. Point E is outside the parallelogram, but BE still gives the correct perpendicular distance needed for area calculation.

Q: Why can't I use the slanted sides to find the area?

The slanted sides are not perpendicular to the base! Area formula requires the perpendicular height - the shortest distance between parallel sides, which is always 90° to the base.

Q: How do I know BE = 6 cm is really the height?

The problem states BE is the external height, and the diagram shows BE drawn perpendicular to the extended base AB. This perpendicular distance is exactly what we need for the area formula.

Q: What if the height was drawn inside the parallelogram instead?

It doesn't matter! Whether the height is drawn inside or outside the parallelogram, as long as it's perpendicular to the base, it gives the same measurement and same area result.

Parallelogram Area with External Height

ABCD is a parallelogram.

BE is its external height.

AD = 3 cm
BE = 6 cm

Calculate the area of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's calculate the area of the parallelogram.

00:15 We'll use the formula. Area equals height times the length of the side. Ready?

00:25 First, identify the side that is the height of the parallelogram.

00:31 Substitute the given values into the formula, calculate, and solve.

00:37 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABCD is a parallelogram.

BE is its external height.

AD = 3 cm
BE = 6 cm

Calculate the area of the parallelogram.

Step-by-step solution

To solve this problem, we proceed with the following steps:

Step 1: Identify the base of the parallelogram as $AD = 3 \, \text{cm}$ .
Step 2: Identify the external height as $BE = 6 \, \text{cm}$ .
Step 3: Use the area formula for the parallelogram: $\text{Area} = \text{Base} \times \text{Height}$
Step 4: Substitute the given measurements into the formula: $\text{Area} = 3 \, \text{cm} \times 6 \, \text{cm}$
Step 5: Compute the area: $\text{Area} = 18 \, \text{cm}^2$

Therefore, the area of the parallelogram is $18 \, \text{cm}^2$ , which matches the given answer choice.

The correct answer is choice 2: 18 cm².

Final Answer

18 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times perpendicular height
Technique: Use given base AD = 3 cm and height BE = 6 cm
Check: Verify units are consistent and result is $3 \times 6 = 18 \, \text{cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Using a side length instead of perpendicular height
Don't use any slanted side as height = wrong area calculation! The height must be perpendicular (90°) to the base, not just any side length. Always identify the perpendicular distance from base to opposite side.

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

What does 'external height' mean in this problem?

An external height is drawn outside the parallelogram, perpendicular to the base. Point E is outside the parallelogram, but BE still gives the correct perpendicular distance needed for area calculation.

Why can't I use the slanted sides to find the area?

The slanted sides are not perpendicular to the base! Area formula requires the perpendicular height - the shortest distance between parallel sides, which is always 90° to the base.

Does it matter which side I choose as the base?

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

How do I know BE = 6 cm is really the height?

The problem states BE is the external height, and the diagram shows BE drawn perpendicular to the extended base AB. This perpendicular distance is exactly what we need for the area formula.

What if the height was drawn inside the parallelogram instead?

It doesn't matter! Whether the height is drawn inside or outside the parallelogram, as long as it's perpendicular to the base, it gives the same measurement and same area result.

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