Area of a Parallelogram with out cross products

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SUMMARY

The area of a parallelogram defined by the vertices (0,0), (3,1), (2,3), and (5,4) can be calculated without using cross products. The solution involves determining the determinants of matrices formed by the vertex coordinates, leading to an area of 7. Verification of the result can be performed using Mathematica, although manual calculation is also valid for confirming the answer.

PREREQUISITES
  • Understanding of matrix determinants
  • Familiarity with the concept of parallelograms in geometry
  • Basic knowledge of Mathematica for verification
  • Ability to perform manual calculations of area
NEXT STEPS
  • Learn how to calculate determinants of matrices in linear algebra
  • Explore the geometric properties of parallelograms
  • Familiarize yourself with Mathematica for mathematical computations
  • Study alternative methods for calculating areas of polygons
USEFUL FOR

Students studying geometry, educators teaching mathematical concepts, and anyone interested in computational methods for area calculation.

c-murda
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Homework Statement



given the vertices:
(0,0)
(3,1)
(2,3)
(5,4)

Homework Equations



solving without cross products and with mathematica if available


The Attempt at a Solution



Te1=[3]
[1]
Te2=[2]
[3]


[det[Ay]]
________

[det[A]]

get you the solution

i got 7

correct?
 
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Yeah it looks ok. By the way since you have mathematica, couldn't you have verified the answer?
 
Defennder said:
Yeah it looks ok. By the way since you have mathematica, couldn't you have verified the answer?

i don't have mathematica that why i was checking my answer. and to know i could do it by hand.

thanks!
 

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