Calculate Parallelogram Area: 4cm Height × 7cm Base Problem

Parallelogram Area with Base-Height Formula

Given the parallelogram of the figure

What is your area?

7cm7cm7cmAAABBBCCCDDDEEE4cm

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's find the area of the parallelogram.
00:07 To do this, multiply the height, which we'll call A E, by the side, D C.
00:14 Now, plug in the given numbers and calculate the area.
00:25 Great job! That's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the parallelogram of the figure

What is your area?

7cm7cm7cmAAABBBCCCDDDEEE4cm

2

Step-by-step solution

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

A=base×height A = \text{base} \times \text{height}

From the problem, we identify the base as 7cm 7 \, \text{cm} and the height as 4cm 4 \, \text{cm} . Substituting these values into the formula, we get:

A=7cm×4cm=28cm2 A = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2

Therefore, the area of the parallelogram is 28cm2 28 \, \text{cm}^2 .

3

Final Answer

28cm2 28\operatorname{cm}^2

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals base times height, not side lengths
  • Technique: Identify perpendicular height: 7×4=28 cm2 7 \times 4 = 28 \text{ cm}^2
  • Check: Units should be squared and calculation matches diagram measurements ✓

Common Mistakes

Avoid these frequent errors
  • Using slanted side instead of perpendicular height
    Don't multiply base by the slanted side length = wrong area! The slanted side is longer than the actual height. Always use the perpendicular distance between parallel sides as your height measurement.

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.

6664.54.54.5

FAQ

Everything you need to know about this question

Why can't I just multiply any two sides together?

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Because area requires the perpendicular height, not just any side! The slanted sides are longer than the actual height. Think of it like measuring how tall a leaning tower really is - you measure straight up, not along the slant.

How do I know which measurement is the height?

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Look for the perpendicular line in the diagram! Height is always the shortest distance between the parallel sides, shown as a line with a right angle symbol (like the 4cm line in this problem).

What if the parallelogram looks different or is tilted?

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The formula stays the same: A=base×height A = \text{base} \times \text{height} . No matter how tilted the parallelogram is, you always need the perpendicular height, not the slanted sides.

Why is my answer in cm² instead of just cm?

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Because area measures square units! You're finding how many 1cm × 1cm squares fit inside the parallelogram. That's why we write cm2 \text{cm}^2 - it shows you're measuring area, not length.

Can I use a different side as the base?

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

What if I accidentally get 14 or 56 as my answer?

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Check your work! 14 comes from adding 7 + 4 + 3 (perimeter mistake), and 56 comes from 7 × 4 × 2 (doubling the area). Remember: Area = base × height, nothing more!

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