Please help (I already solved graphically)...
I have an area (4132.29m^2) I need to subdivide into two equal area parts (2066.15m^2) with the restraint that it needs to be perpendicular to the bottom side of the polygon. I have solved it graphically, but need some help to solve it mathematically (most likely through simultaneous equations).

Question

joachim · Answer

for those who have geogebra, i attached the file

blockcolder · Answer

First, rotate segment CB counterclockwise by the angle theta so that it is parallel to the x-axis.
The rotation can be represented by a matrix so that you can easily find the coordinates of the other points after the rotation.
You then plot the new points, and we will start our solution from there. =)

blockcolder · Answer

Actually, before you do the rotation, you should translate all of the points so that C lies on the origin. The necessary rotation would be immediately obvious after the translation.

joachim · Answer

I rotated the figure by the angle needed for it to lie on the x-axis. What should I do next?

blockcolder · Answer

Find the equation of lines EA, ED, and DC after the rotation.