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height

Find the height of the cuboid ?

p_2: 1
o = Random(-3, 5)
k = Random(-4, 1)
f = Random(1, 5)
j: false
a: 0
A: (0, 0, 0)
B: (-4, 0, 0)
l = Random(-3, 4)
C: (l, 3, 0)
D: (-4, 3, 0)
g = Line(B, D)
h = Line(D, C)
n = Line(B, A)
m = If(o ≟ 0, p_2, o)
p = Line(C, A)
F: (l, 3, m)
G: (-4, 0, m)
H: (-4, 3, m)
q = OrthogonalLine(G, n, space)
r = OrthogonalLine(H, h, space)
E: (l, 0, m)
s = OrthogonalLine(E, n, space)
t = Line(F, C)
b = Line(E, G)
c = Line(H, F)
d = Line(E, F)
e = Line(G, H)
I = Intersect(e, r)
J = Intersect(q, b)
K = Intersect(s, b)
L = Intersect(t, c)
M = Intersect(g, r)
N = Intersect(q, n)
O = Intersect(s, n)
P = Intersect(t, p)
f_1 = Segment(J, I)
g_1 = Segment(K, L)
h_1 = Segment(O, P)
i_1 = Segment(N, M)
j_1 = Segment(N, O)
k_1 = Segment(M, P)
l_1 = Segment(N, J)
m_1 = Segment(M, I)
n_1 = Segment(I, L)
p_1 = Segment(J, K)
q_1 = Segment(K, O)
r_1 = Segment(P, L)
i = Random(-4, -1)
u: ((i_1 * j_1) * l_1)
text4: "Volume = " + u + " unit³"
text1: "" + (LaTeX[m_1]) + " \; unit"