GM 22. Du losange au rectangle
Author: Frédéric Chanez

Découpage

Corrigé

Côté rectangle = grande diagonale

Côté rectangle = petite diagonale

Côté rectangle = côté losange

avec formules

D

d/2

Aire = D ·  \frac{ d }{2 } 

d

D/2

Aire =  \frac{ D }{2 }·d 

Base

Base

hauteur

Aire = B ∙ h

autre possibilité

Aire =  \frac{ D·d }{2 } 

Aire du losange = 1/2 de l'aire du rectangle

A = (-2, 1)
B = (6, 1)
a = LineBisector(A, B)
b = Segment(A, B)
C = Intersect(a, b)
D = Point(a)
c = Circle(C, D)
E = Intersect(c, a, 2)
poly1, a_1, d, b_1, e = Polygon(A, D, B, E)
f = Segment(D, E)
poly2, c_1, a_2, d_1 = Polygon(A, D, C)
poly3, b_2, c_2, d_2 = Polygon(C, D, B)
F = Midpoint(a_1)
G = (0, 0)
u = Vector(F, G)
A'_1 = Translate(A, u)
D'_1 = Translate(D, u)
C'_1 = Translate(C, u)
poly2', c', a', d' = Polygon(A'_1, D'_1, C'_1)
H = Midpoint(d)
I = (4.0837056777278296, -0.12528388639155905)
v = Vector(H, I)
C'_2 = Translate(C, v)
D' = Translate(D, v)
B'_1 = Translate(B, v)
poly3', b', c'_1, d'_1 = Polygon(C'_2, D', B'_1)
J = Midpoint(b_1)
K = Midpoint(e)
poly4, b_3, e_1, c_3 = Polygon(E, C, B)
poly5, a_3, e_2, c_4 = Polygon(E, C, A)
L = (0, 2)
M = (4, 2)
w = Vector(J, M)
z = Vector(K, L)
E'_1 = Translate(E, z)
C'_3 = Translate(C, z)
A' = Translate(A, z)
poly5', a'_1, e', c'_2 = Polygon(E'_1, C'_3, A')
C'_4 = Translate(C, w)
B'_2 = Translate(B, w)
g = false
h = Line(A, f)
i = Line(E, b)
j = Line(B, f)
N = Intersect(i, j)
O = Intersect(h, i)
poly6, a_4, b_4, n, o = Polygon(A, B, N, O)
k = false
l = 3 (slider from -3 to 3, step 1)
m = Line(D, b)
P = Intersect(j, m)
poly7, e_3, d_3, p, n_1 = Polygon(E, D, P, N)
E' = Translate(E, w)
C' = Translate(C, w)
B' = Translate(B, w)
poly4', b'_1, e'_1, c'_3 = Polygon(E', C', B')
q = OrthogonalLine(E, a_1)
r = Line(A, D)
s = OrthogonalLine(B, r)
Q = Intersect(q, r)
R = Intersect(r, s)
poly8, e_4, q_1, r_1, b_5 = Polygon(E, Q, R, B)
t = false
f_1 = Segment(A, B)
g_1 = Segment(E, C)
h_1 = Segment(D, E)
i_1 = Segment(C, B)
j_1 = Segment(A, D)
k_1 = Segment(E, B)
l_1 = Segment(Q, E)
S = Intersect(h, m)
poly9, o_1, n_2, p_1, s_1 = Polygon(O, N, P, S)