Find area using vectors (cross product)

[solina]

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.

Homework Equations

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=$\frac{1}{2}$(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.

 

[jedishrfu]

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>

...

 

[LCKurtz]

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.

Homework Equations

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=$\frac{1}{2}$(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?