How Do You Calculate the Area of a Triangle Using the 0.5*b*h Formula?

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SUMMARY

The area of a triangle can be calculated using the formula 0.5 * b * h, where 'b' is the base and 'h' is the height. In the discussion, a user initially calculated the area incorrectly as 10.64483443 instead of the expected 10.5 due to misidentifying the height. The correct height should be determined by finding the altitude, which is the perpendicular line from the vertex to the base, rather than using the median. Understanding the distinction between median and altitude is crucial for accurate area calculation.

PREREQUISITES
  • Understanding of triangle properties, specifically base and height
  • Knowledge of medians and altitudes in geometry
  • Familiarity with basic arithmetic operations
  • Ability to visualize geometric figures and their dimensions
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  • Learn how to accurately identify the altitude of a triangle
  • Study the properties of medians and altitudes in triangles
  • Practice calculating the area of various triangle types using the formula 0.5 * b * h
  • Explore geometric visualization tools to better understand triangle dimensions
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Could anyone tell me how they found the area of the triangle?

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When I try to use 0.5*b*h I get 10.64483443, not 10.5
 
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They subtracted the areas of the three right triangles outside the given triangle from the area of the rectangle.

How did you calculate b and h for the triangle? I'm guessing you did it wrong.
 
LCKurtz said:
They subtracted the areas of the three right triangles outside the given triangle from the area of the rectangle.

How did you calculate b and h for the triangle? I'm guessing you did it wrong.

I found the midpoint of the two bottom verticies of the triangle, then found the length from that midpoint to the top vertex and used that as the height. The length of the two bottom vertices I used as the base.

I see what they done now, thanks, but is how could I have done using the b*h*0.5?
 
phospho said:
I found the midpoint of the two bottom verticies of the triangle, then found the length from that midpoint to the top vertex and used that as the height. The length of the two bottom vertices I used as the base.

I see what they done now, thanks, but is how could I have done using the b*h*0.5?

You mean "did".

The line from the midpoint of a side to the opposite vertex is a median. Medians are not generally perpendicular to the side, so its length is not the height of the triangle.

To do it that way you would have to find where the line from the vertex perpendicular to the other side intersects the other side and use that line (called the altitude) for the height.
 
LCKurtz said:
You mean "did".

The line from the midpoint of a side to the opposite vertex is a median. Medians are not generally perpendicular to the side, so its length is not the height of the triangle.

To do it that way you would have to find where the line from the vertex perpendicular to the other side intersects the other side and use that line (called the altitude) for the height.

apologies for my bad grammar.

thanks for helping.
 

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