Calculate Parallelogram Area: Base 8 and Height 5 Units

Q: What's the difference between height and slanted side?

The height is the perpendicular distance between parallel sides, shown as a vertical line in the diagram. The slanted side is longer and connects vertices at an angle. Always use height for area calculations!

Q: How do I identify the base and height from a diagram?

Look for the horizontal line labeled with a number (that's your base). The height is shown as a perpendicular line with a right angle symbol, connecting the base to the opposite side.

Q: 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 chosen base. The area will always be the same: $ \text{Area} = \text{base} \times \text{height} $

Q: Why is the area 40 and not 26 or 20?

Because $ 8 \times 5 = 40 $. The wrong answers come from: 26 (adding instead of multiplying), 20 (using wrong measurements), or claiming it's impossible (missing the clear measurements given).

Q: Does the shape being slanted affect the area?

No! Whether the parallelogram is slanted or upright doesn't change the area calculation. As long as you use the correct base and perpendicular height, the formula works the same way.

Parallelogram Area with Base-Height Formula

Calculate the area of the parallelogram using the data in the figure:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of the parallelogram

00:03 Since the sides are parallel, we can draw the height

00:06 We'll use the formula for calculating the area of a parallelogram (base times height)

00:09 We'll substitute the appropriate values and solve for the area

00:11 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the area of the parallelogram using the data in the figure:

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the base and height from the information provided.
Step 2: Apply the formula for the area of a parallelogram.
Step 3: Calculate the area by multiplying the base and height.

Now, let's work through each step:
Step 1: The base of the parallelogram is given as $8$ units, and the height is given as $5$ units.
Step 2: We use the formula for the area of a parallelogram: $\text{Area} = \text{base} \times \text{height}$ .
Step 3: Plugging in the given values, we calculate the area as follows:
$\text{Area} = 8 \times 5 = 40$ .

Therefore, the area of the parallelogram is $40$ square units, which corresponds to choice 2.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times height
Technique: Multiply base 8 units by height 5 units = 40
Check: Verify dimensions are perpendicular height, not slanted side ✓

Common Mistakes

Avoid these frequent errors

Using slanted side instead of perpendicular height
Don't use the slanted side length as height = wrong area calculation! The slanted side is longer than the perpendicular height, leading to an overestimated area. Always use the perpendicular distance between parallel sides as the 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 height and slanted side?

The height is the perpendicular distance between parallel sides, shown as a vertical line in the diagram. The slanted side is longer and connects vertices at an angle. Always use height for area calculations!

How do I identify the base and height from a diagram?

Look for the horizontal line labeled with a number (that's your base). The height is shown as a perpendicular line with a right angle symbol, connecting the base to the opposite side.

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 chosen base. The area will always be the same: $\text{Area} = \text{base} \times \text{height}$

Why is the area 40 and not 26 or 20?

Because $8 \times 5 = 40$ . The wrong answers come from: 26 (adding instead of multiplying), 20 (using wrong measurements), or claiming it's impossible (missing the clear measurements given).

Does the shape being slanted affect the area?

No! Whether the parallelogram is slanted or upright doesn't change the area calculation. As long as you use the correct base and perpendicular height, the formula works the same way.

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