Triangle Area Calculation: Finding Area with Height 7 and Base 8.5

Triangle Area with Insufficient Data

Calculate the area of the triangle below, if possible.

8.58.58.5777

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Step-by-step video solution

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00:00 If possible, calculate the area of the triangle
00:03 The line drawn is not the height, therefore the area cannot be calculated
00:07 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the area of the triangle below, if possible.

8.58.58.5777

2

Step-by-step solution

The formula to calculate the area of a triangle is:

(side * height corresponding to the side) / 2

Note that in the triangle provided to us, we have the length of the side but not the height.

That is, we do not have enough data to perform the calculation.

3

Final Answer

Cannot be calculated

Key Points to Remember

Essential concepts to master this topic
  • Formula: Triangle area = 12×base×height \frac{1}{2} \times \text{base} \times \text{height}
  • Requirements: Need both base AND perpendicular height to that base
  • Check: Verify you have perpendicular height, not just a side length ✓

Common Mistakes

Avoid these frequent errors
  • Using any given measurement as height
    Don't assume the measurement 7 is the height just because it's labeled = wrong calculation! This side measurement isn't perpendicular to the base of 8.5. Always verify you have the perpendicular height to your chosen base before calculating area.

Practice Quiz

Test your knowledge with interactive questions

Complete the sentence:

To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.

FAQ

Everything you need to know about this question

Why can't I use the side length of 7 as the height?

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The height must be perpendicular (at a 90° angle) to the base! The measurement 7 appears to be a side of the triangle, not the perpendicular distance from the opposite vertex to the base.

How do I know if a measurement is height or just a side?

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Look for a right angle symbol (⊥) or a dashed line showing the perpendicular drop. Heights are always drawn at 90° angles to the base, while sides connect the vertices directly.

What information would I need to solve this problem?

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You need either:

  • The perpendicular height to the base of 8.5
  • Enough information to calculate that height (like angles and other sides)

Is there any way to find the area with what's given?

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No, not with this information alone. While you have two measurements, neither gives you the perpendicular height needed for the area formula. You'd need additional data like angles or confirmation that one measurement is actually the height.

What if this was a right triangle?

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If it were a right triangle, then the two perpendicular sides would be the base and height! But this triangle doesn't show a right angle, so we can't make that assumption.

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