Algeo ..question...HELP

[tea217]

Diagram
angle A = 80 degrees, angle C = 30 degrees
AB = AD = 8, BC = CD = 12

Question: Find the area of that diagram using 'cross product' method.

So...the solution is...(2 solutions)
1) divide the polygon in half with a line from B to D. Therefore, you get two triangles. You find their area.
[|8|x|8|x Sin80degree]/2 = 31.5
[|12|x|12|x Sin30degree]/2 = 36
Add up the 2 areas and you get 67.5

2) divide the polygon in half with a line from A to C. Therefore, you get two triangles. You find their area.
[|8|x|12|x Sin125degree]/2 = 39
[|8|x|12|x Sin125degree]/2 = 39
Add up the 2 areas and you get 78

My questions is why doesn't the two areas match?? These 2 ways of getting the area of the polygon are both correct.

 

[Viper0329]

ok...

 

[spanky]

did not work for me...

 

[Viper0329]

i dragged the e and it worked

 

[Drew1082]

what is it supposed to be?

 

[tea217]

Sorry guys, i know my link didn't work b4, cuz i didn't know how to link it...><
Now i fixed it...

 

[tea217]

Any one.......?
Algebra/Geometry....is not hard.....c'mon....help me...

 

[tea217]

Any one.......?
Algebra/Geometry....is not hard.....c'mon....help me...

 

[Haircut]

The two methods used to get the area are correct, it is the polygon that is not correct.
Is this a set question or something that you have just made up?

Split the shape along the line from A to C, you now have a triangle with angles 40, 125 and 15 degrees.
The side opposite the 40 degree angle has length of 12.
Side opposite the 15 degree angle has length of 8.
Sine rule says then that:
12/sin 40=8/sin 15
This is not the case, so this triangle cannot exist, therefore the shape cannot exist.

 

[tea217]

Oh yeahhh......i've never noticed that....
that 12/sin 40=8/sin 15 is wrong..

Haircut..this is not a set of equations i made up...is the cross product.
Say..a and b are two vectors, and y is the angle between these two vectors ( tail to tail)
so.. a x b = |a| |b| sin y.
This definition of the cross product gives the areas of a parallelogram...and if dividied by 2, it gives you area of triangle.

Man...this stupid diagram..got me thinking all day...and it is not a possible shape...
and my teacher said he doesn't know why when i asked him....