Calculate Parallelogram Area: Using 7cm Base and 4cm External Height

Q: What's the difference between external height and slant height?

External height is the perpendicular distance between parallel sides, while slant height is the length of the slanted side. Only the perpendicular height gives the correct area!

Q: Why is BE called 'external' height?

It's called external because point E lies outside the parallelogram. The height line BE extends beyond the parallelogram's boundary to form a right angle with the base.

Q: Can I use any side as the base?

Yes! You can use any side as the base, but you must use the corresponding perpendicular height to that base. Different base = different height measurement.

Q: What if I multiply base times slant side by mistake?

You'll get a larger answer than correct because the slant side is always longer than the perpendicular height. Always look for the right angle symbol (⟂) to identify true height.

Q: How do I remember the area formula?

Think: Area = Base × Height works for rectangles, and parallelograms are just 'tilted rectangles'! The key is using perpendicular height, not slant distance.

Area Formula with External Height

ABCD is a parallelogram.

BE is its external height.

DC = 7 cm
BE = 4 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 find the area of the parallelogram.

00:15 We use the formula: area equals height times base length. Are you ready?

00:27 Next, we plug in the values for the height and the length of the base.

00:31 Now, let’s calculate these numbers to find the solution.

00:40 And there you have it! That's how we solve this question.

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.

DC = 7 cm
BE = 4 cm

Calculate the area of the parallelogram.

Step-by-step solution

To solve this problem, we'll use the formula for the area of a parallelogram:

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

Here, the base $DC$ is given as 7 cm, and the height $BE$ is given as 4 cm.

Now, substituting the known values into the formula, we get:

$\text{Area} = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2$

Thus, the area of the parallelogram is $\boxed{28 \, \text{cm}^2}$ .

Final Answer

28 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times height
Technique: Use perpendicular height, not slant side: 7 × 4 = 28
Check: Units should be square units: cm × cm = cm² ✓

Common Mistakes

Avoid these frequent errors

Using slant side instead of perpendicular height
Don't use the slanted side AD as height = wrong area! The slant side is longer than the perpendicular distance and gives an overestimate. Always use the perpendicular distance (external height BE) as the true 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

What's the difference between external height and slant height?

External height is the perpendicular distance between parallel sides, while slant height is the length of the slanted side. Only the perpendicular height gives the correct area!

Why is BE called 'external' height?

It's called external because point E lies outside the parallelogram. The height line BE extends beyond the parallelogram's boundary to form a right angle with the base.

Can I use any side as the base?

Yes! You can use any side as the base, but you must use the corresponding perpendicular height to that base. Different base = different height measurement.

What if I multiply base times slant side by mistake?

You'll get a larger answer than correct because the slant side is always longer than the perpendicular height. Always look for the right angle symbol (⟂) to identify true height.

How do I remember the area formula?

Think: Area = Base × Height works for rectangles, and parallelograms are just 'tilted rectangles'! The key is using perpendicular height, not slant distance.

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