Calculate Parallelogram Area with Base 8 and Height 6: Geometric Problem

Parallelogram Area with Missing Height Measurement

Find the area of the parallelogram based on the data in the figure:

888666

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Step-by-step video solution

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00:00 Find the area of the parallelogram
00:01 The height is not for the given side, there is not enough data to calculate

Step-by-step written solution

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1

Understand the problem

Find the area of the parallelogram based on the data in the figure:

888666

3

Final Answer

It is not possible to calculate.

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Parallelogram area equals base times perpendicular height
  • Key Issue: Height 6 is not perpendicular to base 8
  • Check: Verify height line is perpendicular to base ✓

Common Mistakes

Avoid these frequent errors
  • Using any side as height
    Don't multiply base 8 × side 6 = 48! The 6 represents a slanted side, not perpendicular height. Always ensure the height measurement is perpendicular to the base.

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 8 × 6 = 48?

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The number 6 represents a slanted side, not the perpendicular height! For parallelogram area, you need the vertical distance between parallel sides, not the length of a slanted side.

How do I find the perpendicular height?

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Look for a right angle symbol (small square) or a dashed line showing the shortest distance between parallel sides. Without this measurement, you cannot calculate the area.

What makes this problem impossible to solve?

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The figure only shows the base length (8) and a slanted side (6). We're missing the crucial perpendicular height measurement needed for the area formula.

Could the area ever be 24 or 28?

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Only if the perpendicular height happened to be exactly 3 or 3.5 respectively. But since we don't know the actual height, we can't determine if these are correct.

What would I need to solve this problem?

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  • The perpendicular height (vertical distance between parallel sides)
  • Or an angle measurement to calculate the height using trigonometry
  • Or coordinates of all vertices

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