Volume d'un prisme à base triangulaire

Rotation d'axe i

Rotation d'axe v

paramètres de la perspective

Bouger le curseur pour faire pivoter la copie.

En dupliquant le prisme et en faisant pivoter la copie autour de l'axe (AB)
on obtient un prisme dont la base est un parallélogramme. Son volume est :
aire du parallélogramme x hauteur.

D'où : Volume du prisme initial :

    aire du parallélogramme x hauteur : 2

ou encore

              aire du triangle x hauteur

Bougez les points rouges !

O = Intersect(xAxis, yAxis)
I_α = (-4, 0)
ρ = (-3.5, 0)
c_α = Circle(I_α, ρ)
M_α = Point(c_α)
verticale = Line(I_α, yAxis)
E_α = Intersect(c_α, verticale, 1)
α = Angle(E_α, I_α, M_α)
I = Point(xAxis)
J = Point(yAxis)
i = Vector(I)
j = Vector(J)
v: cos(α) * j
ell_{α,1}: x^(2) + y^(2) / cos(α)^(2) = 1
ell_{α,2}: x^(2) + y^(2) / sin(α)^(2) = 1
v': -sin(α) * j
I_β = (-2, 0)
transl = Vector(I_α, I_β)
c_β = Translate(c_α, transl)
M_β = Point(c_β)
E_β = Translate(E_α, transl)
β = Angle(E_β, I_β, M_β)
u: cos(β) * i - sin(α) * sin(β) * j
w: -sin(β) * i - sin(α) * cos(β) * j
A_{h,g} = (-5, 1.5)
A_{b,g} = (-5, -1.5)
A_{b,d} = (1.5, -1.5)
A_{h,d} = (1.5, 1.5)
Cadre, l, m, n, o = Polygon(A_{h,g}, A_{b,g}, A_{b,d}, A_{h,d})
Q = (3.620576131687243, 2.729629629629628)
R: Q + 2 * u + w
T: Q + 3 * w
Q'_1: Q + 3 * v
R'_1: R + 3 * v
T'_1: T + 3 * v
face4, r'_2, q'_1, q, r_1 = Polygon(R'_1, Q'_1, Q, R)
face5, q'_2, t'_2, t_2, q_2 = Polygon(Q'_1, T'_1, T, Q)
a_4 = Segment(T, T'_1)
b_1 = Segment(Q'_1, R'_1)
b_2 = Segment(R'_1, R)
b_3 = Segment(R, Q)
b_4 = Segment(Q, Q'_1)
h_3 = Segment(Q'_1, T'_1)
h_2 = Segment(Q, T)
poly1, t', t, r, r' = Polygon(T'_1, T, R, R'_1)
a = Segment(T'_1, R'_1)
b = Segment(T, R)
c = Segment(R'_1, R)
A = Midpoint(a)
B = Midpoint(b)
γ = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
poly2, q', t'_1, r'_1 = Polygon(T'_1, R'_1, Q'_1)
T'' = Rotate(T'_1, γ, A)
R'' = Rotate(R'_1, γ, A)
Q'' = Rotate(Q'_1, γ, A)
poly2', q'', t'', r'' = Polygon(T'', R'', Q'')
poly3, q_1, t_1, r_2 = Polygon(T, R, Q)
T' = Rotate(T, γ, B)
R' = Rotate(R, γ, B)
Q' = Rotate(Q, γ, B)
poly3', q'_3, t'_3, r'_3 = Polygon(T', R', Q')
e = Segment(Q'', Q')
f = Segment(R'', R')
g = Segment(T'', T')
C: A + v
D: B - v
d = Segment(C, D)