9 GM 47 : Bandes de parallélogrammes
Author: Frédéric Chanez

11

Aires

Hauteurs

A = (2, 6)
a = OrthogonalLine(A, xAxis)
C = Point(a)
k = Circle(C, 2)
N = Intersect(k, a, 1)
B = (13, 6)
b = OrthogonalLine(B, xAxis)
D = (4, 5)
E = (8, 3)
F = (11, 6)
G = Point(b)
c = PolyLine(C, D, E, F, G)
H = Point(a)
u = Vector(C, N)
C' = Translate(C, u)
D' = Translate(D, u)
E' = Translate(E, u)
F' = Translate(F, u)
G' = Translate(G, u)
c' = PolyLine(C', D', E', F', G')
poly1, d, h, j, l = Polygon(C, D, D', N)
poly2, d_1, e, e', d'_1 = Polygon(D, E, E', D')
poly3, e_1, f, f', e'_1 = Polygon(E, F, F', E')
poly4, f_1, g, g', f'_1 = Polygon(F, G, G', F')
I = Point(a)
J = (6, -1)
K = (11, 1)
L = Point(b)
i = PolyLine(I, J, K, L)
p = Circle(I, 2)
M = Intersect(p, a, 1)
v = Vector(I, M)
I' = Translate(I, v)
J' = Translate(J, v)
K' = Translate(K, v)
L' = Translate(L, v)
i' = PolyLine(I', J', K', L')
poly5, i_1, j_1, j', m = Polygon(I, J, J', M)
poly6, j_2, k_1, k', j'_1 = Polygon(J, K, K', J')
poly7, k_2, l_1, l', k'_1 = Polygon(K, L, L', K')
n = Line(D, a)
q = Line(E, a)
r = Line(F, a)
s = OrthogonalLine(C, n)
t = OrthogonalLine(D, q)
a_1 = OrthogonalLine(E, q)
b_1 = OrthogonalLine(F, r)
O = Intersect(n, s)
c_1 = Segment(C, O)
P = Intersect(q, t)
g_1 = Segment(D, P)
h_1 = Segment(P, E)
m_1 = Segment(O, D)
Q = Intersect(r, a_1)
n_1 = Segment(E, Q)
p_1 = Segment(Q, F)
R = Intersect(b, b_1)
q_1 = Segment(F, R)
r_1 = Segment(R, G)
s_1 = Segment(E, Q)
t_1 = Line(J, a)
a_2 = Line(K, a)
b_2 = OrthogonalLine(I, a)
c_2 = OrthogonalLine(J, a)
d_2 = OrthogonalLine(K, a)
S = Intersect(t_1, b_2)
e_2 = Segment(I, S)
f_2 = Segment(S, J)
T = Intersect(a_2, c_2)
g_2 = Segment(J, T)
h_2 = Segment(T, K)
U = Intersect(b, d_2)
i_2 = Segment(K, U)
l_2 = Segment(U, L)
m_2 = Segment(S, J)
V = (2, -4)
W = (13, -4)
w = Vector(V, W)
z = Vector(W, V)
o = true
o_1 = false
aire_1: poly1 + poly2 + poly3 + poly4
Aire_2: poly5 + poly6 + poly7
texte2: "Aire = " + e_2 + "·" + m + " + " + g_2 + "·" + m + " + " + i_2 + "·" + m + " 
Aire = " + Aire_2 + " cm²"
texte1: "Aire = " + c_1 + "·2 + " + g_1 + "·" + l + " + " + s_1 + "·2 + " + q_1 + "·" + l + " 
Aire = " + aire_1 + " cm²"