Calculate Parallelogram Area: 7-Unit Base with 9-Unit Height

Area Formula with Perpendicular Height

Calculate the area of the parallelogram below:

777999AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's start by finding the area of the parallelogram. Ready?
00:11 Remember, in a parallelogram, opposite sides are equal. This is important, so keep that in mind.
00:24 Now, to calculate the area, we multiply the height, that's line D E, by the base, which is side A B.
00:41 Let's plug in the values we have and solve it step by step to find the area.
00:48 And that's how we find the solution. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the area of the parallelogram below:

777999AAABBBCCCDDDEEE

2

Step-by-step solution

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

  • Step 1: Identify the base and the height of the parallelogram.
  • Step 2: Apply the formula for the area of a parallelogram.
  • Step 3: Calculate the area using the provided measurements.

Now, let's work through each step:

Step 1: The base of the parallelogram is given as 77 cm, and the height corresponding to this base is 99 cm.

Step 2: We'll use the formula for the area of a parallelogram, which is Area=base×height \text{Area} = \text{base} \times \text{height} .

Step 3: Plugging in our values, we get:

Area=7cm×9cm=63cm2 \text{Area} = 7 \, \text{cm} \times 9 \, \text{cm} = 63 \, \text{cm}^2

Therefore, the correct solution to the problem is 63cm2 63 \, \text{cm}^2 .

3

Final Answer

63 63 cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of parallelogram equals base times perpendicular height
  • Technique: Use 7×9=63 7 \times 9 = 63 cm² with given measurements
  • Check: Verify height is perpendicular to base, not slanted side ✓

Common Mistakes

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

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the parallelogram according to the data in the diagram.

101010777AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

Why can't I use the slanted side as the height?

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The height must be perpendicular to the base! The slanted side is longer than the true height. Think of it like measuring the altitude of a mountain - you measure straight up, not along the slope.

How do I know which measurement is the base and which is the height?

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In this diagram, the base is 7 units (horizontal bottom) and the height is 9 units (vertical line with the right angle symbol). The height is always perpendicular to the base.

Does it matter which side I choose as the base?

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No! You can use any side as the base, but you must use the corresponding perpendicular height to that base. The area will always be the same.

What if the parallelogram looks tilted or slanted?

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The shape doesn't change the formula! Whether it's tilted or not, Area = base × perpendicular height. Just make sure you identify the correct perpendicular height.

How is this different from a rectangle's area?

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It's exactly the same formula! A rectangle is just a special parallelogram where all angles are 90°. Both use Area=base×height \text{Area} = \text{base} \times \text{height} .

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