Calculate Parallelogram Area: 7 cm Base with 3.5 cm Height

Q: What's the difference between height and side length in a parallelogram?

Height is the perpendicular distance between parallel sides, while side length is the actual length of a slanted side. Always use height for area calculations, not the slanted side!

Q: Why do I multiply base times height for area?

The parallelogram area formula $ A = b \times h $ works because you can reshape any parallelogram into a rectangle with the same base and height, giving the same area.

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 height perpendicular to that base. Different base-height pairs will give the same area.

Q: How do I know if the height is perpendicular?

Look for right angle symbols (small squares) in the diagram, or dashed lines showing the perpendicular distance. The height line should form 90° angles with the base.

Parallelogram Area with Base-Height Multiplication

AB = 7 cm

Height of the rectangle = 3.5 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

00:08 Let's calculate the area of parallelogram A B C D.

00:12 Remember, in a parallelogram, opposite sides are equal.

00:22 We'll use the formula for the area of a parallelogram.

00:26 It's base times height. So, side C D multiplied by height H.

00:31 Let's plug in the given values and calculate the area.

00:42 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

AB = 7 cm

Height of the rectangle = 3.5 cm

Calculate the area of the parallelogram.

Step-by-step solution

To calculate the area of the parallelogram, we will use the formula:

Step 1: Identify provided values:
- Base $b = 7$ cm
- Height $h = 3.5$ cm

Step 2: Substitute into the area formula:
$\text{Area} = b \times h = 7 \times 3.5$

Step 3: Perform the calculation:
$\text{Area} = 24.5 \, \text{cm}^2$

Therefore, the area of the parallelogram is 24.5 cm $^2$ .

Final Answer

24.5 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times height for parallelograms
Technique: Multiply base 7 cm by perpendicular height 3.5 cm
Check: Units should be square units: 7 × 3.5 = 24.5 cm² ✓

Common Mistakes

Avoid these frequent errors

Using slant side instead of perpendicular height
Don't measure the slanted side length as height = wrong area calculation! The slant side is longer than the perpendicular distance, giving an area that's too large. Always use the perpendicular height from base to 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

What's the difference between height and side length in a parallelogram?

Height is the perpendicular distance between parallel sides, while side length is the actual length of a slanted side. Always use height for area calculations, not the slanted side!

Why do I multiply base times height for area?

The parallelogram area formula $A = b \times h$ works because you can reshape any parallelogram into a rectangle with the same base and height, giving the same area.

Does it matter which side I choose as the base?

No! You can use any side as the base, but you must use the height perpendicular to that base. Different base-height pairs will give the same area.

How do I know if the height is perpendicular?

Look for right angle symbols (small squares) in the diagram, or dashed lines showing the perpendicular distance. The height line should form 90° angles with the base.

What if I get a decimal answer like 24.5?

Decimal areas are perfectly normal! Just make sure to include the correct square units (cm², m², etc.) and round appropriately if needed.

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