GM 22. Du trapèze au parallélogramme
Author: Frédéric Chanez

B

B

b

B

b

h

b

B

b

Formule générale

Aire du parallélogramme =

Aire du trapèze =

Aire du trapèze = 

$ \frac{(B+b)·h}{2} $

C = (6, 3)
B = (8, -2)
A = (-1, -2)
h = Line(A, B)
a = Segment(A, B)
b = Line(C, a)
D = Point(b)
poly1, a_1, b_1, c, d = Polygon(A, B, C, D)
E = (16, -5)
u = Vector(B, E)
A' = Translate(A, u)
B' = Translate(B, u)
C' = Translate(C, u)
D' = Translate(D, u)
poly1', a', b', c', d' = Polygon(A', B', C', D')
e = Circle(E, C')
F = Point(e)
α = Angle(F, E, C')
A'' = Rotate(A', -α, E)
B'' = Rotate(B', -α, E)
C'' = Rotate(C', -α, E)
D'' = Rotate(D', -α, E)
poly1'', a'', b'', c'', d'' = Polygon(A'', B'', C'', D'')
G = Point(h)
f = OrthogonalLine(G, h)
H = Intersect(b, f)
g = Segment(H, G)
Textepoly1: "Aire " + (Name[A]) + (Name[B]) + (Name[C]) + (Name[D]) + " = " + poly1
texte3: "Aire " + (Name[A]) + (Name[B]) + (Name[C]) + (Name[D]) + " = " + poly1
i: 2 * poly1
j = Segment(A, B)
k = Segment(D, C)
m = Segment(A'', E)
n = Segment(D'', F)
o = false
l = Segment(G, H)
p = false
q = false
r = false
texte2: "(" + a + "+" + c'' + ")·" + g + " = " + i + " cm²"
texte1: " \frac{(" + (LaTeX[a]) + "+" + (LaTeX[c]) + ")·" + (LaTeX[g]) + "}{2} = " + (LaTeX[poly1]) + "   \; cm^2"