How to divide a right trapezoid into 2 equal area? (photo)?

The link below should give you the details you need.

Construct a line from the lower left corner to the upper right corner, or lower right corner to upper left corner.

The picture is blur , it looks to me that
A = 552cm
B = 409cm (You wrote B = 209cm , I think it was typo .)
C = 572cm
D = 261cm
The area = 184928cm^2 (You wrote the area is 184926 cm^2 .)

B and D are perpendicular to A , so C becomes
C^2 = A^2 + (B - D)^2 = 3226608
C = 571.496... [cm]
But I do not use this value .

Next , the area becomes
(1/2)(B + D)*A = 184920 [cm^2]
I assume that this is the correct value .

Next , put the right trapezoid as A is on the x-axis and B is on the y-axis .
So the xy-coodinates of the under-left vertex becomes (0,-409) and
the under-right vertex becomes (552,-261) .

Therefore the equation of line C becomes
y = [(-261 - (-409))/552]x - 409
y = (148/552)x - 409

If we draw a vertical cut line from (x,0) then the length of it becomes
0 - [(148/552)x - 409] = -(148/552)x + 409

The area of the left trapezoid becomes
(1/2)[409 - (148/552)x + 409]x
= 409x - (74/552)x^2

It must become the half of the area of the original trapezoid . So
184920 / 2 = 409x - (74/552)x^2
(74/552)x^2 - 409x + 92460 = 0

We can solve it , and x must be 0 < x < 552 . Therefore
x = 245.9 [cm] (approx.)