Parallelogram Length Calculation: Finding BE in a 60 cm² Shape

Q: How do I know which line is the height in a parallelogram?

The height is always the perpendicular distance between parallel sides. In this problem, BE is perpendicular to side AB, making it the correct height measurement.

Q: What if I don't have the area but need to find it?

Simply multiply the base times height: $ \text{Area} = \text{base} \times \text{height} $. Make sure both measurements use the same units!

Q: Is the height always drawn inside the parallelogram?

Not necessarily! Sometimes the height line extends outside the parallelogram, especially with obtuse angles. The key is that it's always perpendicular to the base.

Q: Why isn't the area just length times width like a rectangle?

A parallelogram is slanted, so using the slanted side gives you more than the actual height. Only the perpendicular height gives the true vertical distance needed for area calculation.

Parallelogram Area with Height Calculations

The parallelogram ABCD has an area equal to 60 cm².

Calculate the length of BE.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find BE

00:03 opposite sides are equal in a parallelogram

00:20 we'll use the formula for calculating parallelogram area

00:23 side(AD) multiplied by height (BE)

00:35 we'll substitute appropriate values and solve for BE

00:55 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

The parallelogram ABCD has an area equal to 60 cm².

Calculate the length of BE.

Step-by-step solution

To determine the length of $BE$ , the height of the parallelogram $ABCD$ , we can use the formula for the area of a parallelogram:

$\text{Area of a parallelogram} = \text{base} \times \text{height}$

Given:

Area = 60 cm²
Base $AB$ = 12 cm

We need to find $BE$ , the height.

Using the formula, substitute the known values:

$60 = 12 \times BE$

To solve for $BE$ , divide both sides of the equation by 12:

$BE = \frac{60}{12}$

$BE = 5$

Thus, the length of $BE$ is $5$ cm.

Final Answer

$5$ cm

Key Points to Remember

Essential concepts to master this topic

Area Formula: Parallelogram area equals base times height
Technique: Substitute known values: $60 = 12 \times BE$
Check: Verify by multiplying: $12 \times 5 = 60$ cm² ✓

Common Mistakes

Avoid these frequent errors

Using the wrong side as base or height
Don't use any diagonal or slanted side as the base = incorrect area calculation! The height must be perpendicular to the base, not just any line segment. Always identify the base first, then find the perpendicular distance (height) to the 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

How do I know which line is the height in a parallelogram?

The height is always the perpendicular distance between parallel sides. In this problem, BE is perpendicular to side AB, making it the correct height measurement.

Can I use any side as the base?

Yes! You can use any side as the base, but then you must use the perpendicular height to that specific side. The area will always be the same regardless of which base-height pair you choose.

What if I don't have the area but need to find it?

Simply multiply the base times height: $\text{Area} = \text{base} \times \text{height}$ . Make sure both measurements use the same units!

Is the height always drawn inside the parallelogram?

Not necessarily! Sometimes the height line extends outside the parallelogram, especially with obtuse angles. The key is that it's always perpendicular to the base.

Why isn't the area just length times width like a rectangle?

A parallelogram is slanted, so using the slanted side gives you more than the actual height. Only the perpendicular height gives the true vertical distance needed for area calculation.

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Parallelogram Length Calculation: Finding BE in a 60 cm² Shape

Parallelogram Area with Height Calculations

❤️ 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

How do I know which line is the height in a parallelogram?

Can I use any side as the base?

What if I don't have the area but need to find it?

Is the height always drawn inside the parallelogram?

Why isn't the area just length times width like a rectangle?

🌟 Unlock Your Math Potential

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