(c,d)

(a,b)

a

c

b

d

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Find the area of the parallelogram in terms of a, b, c, d.

A = Intersect(xAxis, yAxis)
B = (4.18, 1.44)
a = Segment(A, B)
C = (1.724, 5.15)
b = Segment(A, C)
c = Line(C, a)
d = Line(B, b)
D = Intersect(c, d)
e = Segment(B, D)
f = Segment(D, C)
g = OrthogonalLine(C, xAxis)
h = OrthogonalLine(B, xAxis)
i = OrthogonalLine(B, yAxis)
j = OrthogonalLine(C, yAxis)
E = Intersect(g, xAxis)
F = Intersect(h, xAxis)
G = Intersect(h, j)
H = Intersect(j, yAxis)
I = Intersect(i, yAxis)
J = Intersect(g, i)
poly1, e_1, f_1, g_1, h_1, i_1, j_1 = Polygon(E, F, G, H, I, J)
K = Intersect(yAxis, c)
K' = Mirror(K, C)
H' = Mirror(H, C)
L = Intersect(h, c)
M = Intersect(xAxis, d)
M' = Mirror(M, B)
F' = Mirror(F, B)
N = Intersect(a, j_1)
u = Vector(H', E)
L' = Translate(L, u)
O = Midpoint(N, L')
v = Vector(D, C)
k = 0 (slider from 0 to 1, step 0.01)
poly2, k', c_1, h' = Polygon(C, H', K')
poly3, k'_1, h'_1, g_2, l = Polygon(K', H', G, L)
poly4, l_1, d_1, m', f' = Polygon(L, D, M', F')
poly5, b_1, f'_1, m'_1 = Polygon(F', M', B)
P = Intersect(b, i_1)
poly6, p, j_2, n, a_1 = Polygon(P, J, N, A)
u' = Dilate(u, k, H')
v' = Dilate(v, k, D)
L'_1 = Translate(L, v')
D' = Translate(D, v')
M'' = Translate(M', v')
F'' = Translate(F', v')
poly4', l'_1, d', m'', f'' = Polygon(L'_1, D', M'', F'')
K'' = Translate(K', u')
H'' = Translate(H', u')
G' = Translate(G, u')
L'_2 = Translate(L, u')
poly3', k'', h'', g', l'_2 = Polygon(K'', H'', G', L'_2)
F''_1 = Rotate(F', ((k * 180))°, B)
M''_1 = Rotate(M', ((k * 180))°, B)
B' = Rotate(B, ((k * 180))°, B)
poly5', b', f''_1, m''_1 = Polygon(F''_1, M''_1, B')
C' = Rotate(C, ((k * 180))°, C)
H''_1 = Rotate(H', ((k * 180))°, C)
K''_1 = Rotate(K', ((k * 180))°, C)
poly2', k''_1, c', h''_1 = Polygon(C', H''_1, K''_1)
P' = Rotate(P, ((k * 180))°, O)
J' = Rotate(J, ((k * 180))°, O)
N' = Rotate(N, ((k * 180))°, O)
A' = Rotate(A, ((k * 180))°, O)
poly6', p', j', n', a' = Polygon(P', J', N', A')
poly7, p_1, c_2, g_3, b_2, n_1, j_3 = Polygon(P, C, G, B, N, J)