Hauteur du parallélogramme

Base du parallélogramme

Animation

 Le pavé vert et le prisme bleu ont le même volume

Hauteur du prisme

Hauteur du prisme

Longueur

Largeur

Longueur x Largeur x Hauteur du pavé

=

Base du parallélogramme x Hauteur du parallélogramme x Hauteur du prisme

Retenir : Volume = Aire d'une Base du prisme x Hauteur du prisme

Volume d'un prisme droit dont la base est un parallélogramme

D = (0.4, 5.14)
A = (-4.788457526593981, 5.14)
e = Line(A, D)
v = Vector(A, D)
B = (-2.988457526593981, 2.58)
f = OrthogonalLine(B, e)
E = Intersect(e, f)
α = Angle(E, A, B)
a = -1 (slider from -1 to 3, step 0.01)
u = Vector(B, A)
C = Translate(B, v)
poly1, a_1, b, c, d = Polygon(B, A, D, C)
g = OrthogonalLine(C, e)
F = Intersect(e, g)
poly2, b_1, a_2, e_1 = Polygon(B, E, A)
E'_1 = If(α < 90°, Translate[F, Vector[-a * v]], Translate[E, Vector[a * v]])
B'_1 = If(α < 90°, Translate[D, Vector[-a * v]], Translate[A, Vector[a * v]])
A'_1 = If(α < 90°, Translate[C, Vector[-a * v]], Translate[B, Vector[a * v]])
poly3, a_3, e_2, f_1, d_1 = Polygon(B, E, F, C)
h = Segment(B, E)
i = Segment(B, C)
poly4, b', a', e' = Polygon(A'_1, E'_1, B'_1)
G = (-20.259865692106516, 6.343777952097684)
H = (-15.479865692106522, 10.183777952097685)
w = Vector(G, H)
A' = Translate(A, w)
B'_2 = Translate(B, w)
C'_1 = Translate(C, w)
D' = Translate(D, w)
poly5, a'_1, b'_1, c', d' = Polygon(A', B'_2, C'_1, D')
l = Segment(A, A')
m = Segment(B, B'_2)
n = Segment(C, C'_1)
p = Segment(D, D')
I = Translate(A'_1, w)
E'' = Translate(E'_1, w)
J = Translate(B'_1, w)
poly4', j_1, i_1, e'' = Polygon(I, E'', J)
q = Segment(B'_1, J)
r = Segment(E'_1, E'')
s = Segment(I, A'_1)
B' = Translate(B, w)
E' = Translate(E, w)
F' = Translate(F, w)
C' = Translate(C, w)
poly3', b'_2, e'_1, f', c'_1 = Polygon(B', E', F', C')
t = Segment(E', E)
c_1 = Segment(B', B)
g_1 = Segment(C, C')
K = (6.92, 8.98)
h_1 = Segment(F, K)
L = Point(t)
k = Segment(A, E)
l_1 = Segment(B, A)
M = Point(d')
m_1 = Segment(A, M)
N = Point(d')
n_1 = Segment(M, N)
O = Point(b'_1)
p_1 = Segment(M, O)
P = Point(c)
Q = Point(d)
j = Segment(P, Q)
R = Point(d')
k_1 = Segment(P, R)
S = Point(c')
q_1 = Segment(R, S)
T = Point(d)
r_1 = Segment(T, Q)
U = Intersect(b, h)
s_1 = Segment(U, T)