Find area using vectors (cross product)

  • Thread starter solina
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  • #1
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Homework Statement


Hello, I've been trying to solve this problem, but in the examples that my teacher gave me didn't include something like this, I know how to calculate area but only if I have all the coordinates established.
I need to find the area using the cross product.

Untitled.jpg


Homework Equations


a92ba9287031332f696b2ae85382e1aa.png



The Attempt at a Solution


I know I must divide the polygon into triangles, so I can calculate the area.
I need a starting point for the coordinates.
For example I can call the starting point A.
A(0,0)
Then I need more coordinates in order to establish each vector.
B(0,1.03)
C(0,1.12)

After that...
AB = 0i + 1.03j
AC = 0i + 1.12j
CB = 0i + 2.15j

A=[itex]\frac{1}{2}[/itex](AB x AC)

If what I wrote above is right then I think I can solve It, but I'm almost absolutely sure that is wrong.
I need to know how to declare each vector so I can calculate the area.
I hope is clear enough, and thanks in advance for taking your time to read and help me with this problem.
 

Answers and Replies

  • #2
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Do you know geometrically what area the cross product represents?

Next you need the identify the points on the diagram.

I assume you meant point A to be the one in the lower left
and that the x axis is along the lower left boundary line, correct?

If so then the vectors you've written are wrong:

AB = <1.03, 0>

And

AC = <0, 1.14>

...
 
Last edited:
  • #3
LCKurtz
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Homework Statement


Hello, I've been trying to solve this problem, but in the examples that my teacher gave me didn't include something like this, I know how to calculate area but only if I have all the coordinates established.
I need to find the area using the cross product.

Untitled.jpg


Homework Equations


a92ba9287031332f696b2ae85382e1aa.png



The Attempt at a Solution


I know I must divide the polygon into triangles, so I can calculate the area.
I need a starting point for the coordinates.
For example I can call the starting point A.
A(0,0)
Then I need more coordinates in order to establish each vector.
B(0,1.03)
C(0,1.12)

After that...
AB = 0i + 1.03j
AC = 0i + 1.12j
CB = 0i + 2.15j

A=[itex]\frac{1}{2}[/itex](AB x AC)
That isn't correct without absolute value signs. The area is numerically equal to 1/2 the length of the cross product.

If what I wrote above is right then I think I can solve It, but I'm almost absolutely sure that is wrong.
I need to know how to declare each vector so I can calculate the area.
I hope is clear enough, and thanks in advance for taking your time to read and help me with this problem.
Offhand, I don't think your problem has a solution. I don't think knowing the lengths of the sides of a pentagon is enough information to determine its area. Is there more information you haven't included?
 

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