Base

Animation

Base

D est le milieu de [AB] et E le milieu de [AC]

Le triangle ABC et le parallélogramme DBCF ont la même aire

Le parallélogramme DBCF et le rectangle DHGF ont le même aire

Hauteur

Hauteur : 2

Base

Base x Hauteur

Aire = ----------------------

2

Aire du triangle

Animation

A = (1.3846130536727694, 2.2574212519801273)
B = (3.1063173218083264, -3.590782499442153)
C = (12.474660721288467, -3.650277907555036)
poly1, c, a, b = Polygon(A, B, C)
D = Midpoint(c)
E = Midpoint(b)
F = Mirror(D, E)
d = Segment(A, D)
e = Segment(D, B)
f = Segment(A, E)
g = Segment(E, C)
t = -77.3 (slider from -100 to 700, step 0.1)
h = Line(B, C)
i = OrthogonalLine(D, h)
j = OrthogonalLine(F, h)
G = Intersect(j, h)
H = Intersect(i, h)
poly2, e_1, a_1, d_1 = Polygon(A, D, E)
poly3, e_2, k, l = Polygon(Rotate[D, (-t)°, E], Rotate[A, (-t)°, E], E)
poly4, d_2, b_1, c_1, f_1 = Polygon(D, B, C, F)
poly5, c_2, f_2, g_1 = Polygon(F, G, C)
poly6, b_2, d_3, h_1 = Polygon(D, H, B)
α = Angle(C, B, A)
u = Vector(F, D)
F' = Translate(F, Vector[(t - 300) / 100 * u])
v = Vector(F, F')
poly7 = If(α ≤ 90°, Polygon[Translate[D, Vector[-v]], Translate[H, Vector[-v]], Translate[B, Vector[-v]]], Polygon[Translate[F, v], Translate[G, v], Translate[C, v]])
poly8, d_4, f_3, g_2, h_2 = Polygon(D, F, G, H)
m = OrthogonalLine(A, h)
I = Intersect(m, h)
n = Segment(A, I)
J = Intersect(i, h)
q = Segment(D, J)
w = Vector(B, J)
p = Segment(Translate[B, Vector[(t - 300) / 100 * w]], Translate[C, Vector[(t - 300) / 100 * w]])