SA'B'C'\ est\ une\
réduction\ de\ SABC

ABCA'B'C' \ est \ un\
tronc\ de\ pyramide 

A'

B'

C'

A

B

C

S

MathsEnClair.com

Section\ d'une\ pyramide\ à\ base\ triangulaire

On\ sait\ que\ le\ plan\ de\ section\ est\
parallèle\ à\ la\ base\ de\ la\ grande\
pyramide.

Questions\
Notons\ k\ le\ coefficient\ de\ la\ réduction.\
On\ a:\ 
question\ n°1:\frac {SA'} {SA}=...\
question\ n°2 : \mathcal {V}_{SA'B'C'}=...\times \mathcal {V}_{SABC}.

question\ n°1: \frac {SA'} {SA}=\frac {SB'} {SB}=\frac {SC'} {SC}=k\
question\ n°2 : \mathcal {V}_{SA'B'C'}=k^\textcolor{blue}{3}\times \mathcal {V}_{SABC}

afficher la réponse

A = (1.9484589760633515, 3.3530375740028133)
B = (5.037849432442894, 2.1690795547914905)
a = Segment(A, B)
C = (6.7397890850591695, 3.3530375740028138)
b = Segment(B, C)
c = Segment(C, A)
D = (4.047635043469079, 7.32690016876537)
d = Segment(A, D)
e = Segment(D, B)
f = Segment(D, C)
E = Point(d)
g = Line(E, a)
F = Intersect(g, e)
h = Line(F, b)
G = Intersect(h, f)
i = Segment(E, G)
j = Segment(E, F)
k = Segment(F, G)
poly1, c_1, a_1, b_1 = Polygon(A, B, C)
poly2, g_1, e_1, f_1 = Polygon(E, F, G)
H = (7.703002881230598, 7.908939823296574)
I = (7.038191954099392, 7.49035516547322)
u = Vector(H, I)
J = (8.263112669733031, 4.979322020765612)
K = (7.622924369532615, 4.634605243734615)
v = Vector(J, K)
poly3, d_1, e_2, f_2, g_2 = Polygon(D, E, F, G)
l = true