Cross product to find the area of a triangle

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SUMMARY

The area of a triangle can be calculated using the cross product of two vectors originating from a common vertex. Specifically, the area is determined by taking the magnitude of the cross product of vectors ADB and dividing it by two. However, to find the area of triangle ADC, one cannot simply apply the same method as triangle ABD without additional geometric considerations, as the areas of triangles ABD and ACD may differ based on their respective vertex arrangements.

PREREQUISITES
  • Understanding of vector mathematics
  • Familiarity with cross product operations
  • Knowledge of geometric properties of triangles
  • Basic principles of area calculation in geometry
NEXT STEPS
  • Study the properties of the cross product in vector algebra
  • Learn how to calculate areas of polygons using vector methods
  • Explore geometric interpretations of vector operations
  • Investigate the relationship between triangle areas and their vertex configurations
USEFUL FOR

Students in geometry or physics, educators teaching vector mathematics, and anyone interested in applying vector operations to solve geometric problems.

molly1103
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okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because this is a bit confusing to describe only with words:
for example we have this
http://farside.ph.utexas.edu/teaching/301/lectures/img243.png
and then if we use the cross product of a and b and we find the magnitude of that vector and we divide it by 2 we get the area of the triangle with vertices ADB, so far so good. but i am confused as to how do we find the area of the triangle ADC? my professor said that we can't find it simply by finding the cross product and dividing it by two... anybody can help me with this? :(
thanks!
 
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Look at the two triangles ABD and ACD. Geometrically, how would you calculate their areas? Are these areas different?
 

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