 \frac{ I'J'K'L' }{ A'B'C'D'}= \frac{  I'L'Q'R' }{ A'B'C'D'}+ \frac{ Q'R'J'K' }{A'B'C'D'} 
= \frac{  ILQR }{ ABCD'}+ \frac{ QRJK }{ABCD} = \frac{ IJKL}{ ABCD}

D = (-5.568208780487804, 14.454581463414634)
C = (-1.283038048780487, 13.77934243902439)
B = (-2.893223414634146, 7.754132682926827)
A = (-6.4771843902439015, 10.610913170731706)
poly1, a, b, c, d = Polygon(A, B, C, D)
k = 0.5 (slider from 0 to 0.5, step 0.1)
B' = (6.040708292682928, 7.520396097560974)
e = Line(B, B')
h = Line(A, e)
A' = Point(h)
f = Line(C, e)
g = Line(D, e)
D' = Point(g)
C' = Point(f)
poly2, e_1, g_1, f_1, h_1 = Polygon(B', C', D', A')
I = Midpoint(b)
J = Midpoint(c)
K = Midpoint(d)
L = Midpoint(a)
I' = Midpoint(e_1)
J' = Midpoint(g_1)
K' = Midpoint(f_1)
L' = Midpoint(h_1)
poly3, k_1, l, i, j = Polygon(K, L, I, J)
poly4, o, p, m, n = Polygon(K', L', I', J')
q = Segment(A, C)
r = Segment(A', C')
Q = Intersect(k_1, q)
R = Intersect(i, q)
s = Line(R, h)
t = Line(Q, h)
R' = Intersect(r, s)
Q' = Intersect(r, t)
poly5, o_1, t_1, s_1, n_1 = Polygon(K', Q', R', J')
poly6, t_2, p_1, m_1, s_2 = Polygon(Q', L', I', R')
poly7, t_3, o_2, p_2 = Polygon(K', L', Q')
poly8, s_3, n_2, m_2 = Polygon(J', I', R')