Author: P.Goubet

\frac{ base x hauteur }{2 } 

Aire d'un triangle

Utiliser les curseurs pour construire le rectangle BCH_3H_2

L'aire du rectangle BCH_3H_2 est  :

L'aire du triangle ABC est :

\frac{ BC x AH }{2 } 

=

BC x BH_2

BC x AH

=

a_1 = 2 (slider from 0 to 6, step 0.1)
B = (0, -2)
C = (6, -2)
A: (a_1, 0)
ABC, c, a, b = Polygon(A, B, C)
d = OrthogonalLine(A, a)
H = Intersect(d, a)
e = Segment(A, H)
k = 0 (slider from 0 to 3, step 0.1)
U = (-3, 0)
V: (-3, k)
u = Vector(U, V)
A_1 = Translate(A, u)
B_1 = Translate(B, u)
H_1 = Translate(H, u)
C_1 = Translate(C, u)
f = Segment(A, B_1)
g = Segment(H_1, B)
h = Segment(H_1, C)
i = Segment(A, C_1)
α = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
O_2 = Midpoint(A_1, B)
B_2 = Rotate(B_1, α, O_2)
A_2 = Rotate(A_1, α, O_2)
H_2 = Rotate(H_1, α, O_2)
triangleH_2, d_1, e_1, f_1 = Polygon(A_2, H_2, B_2)
O_3 = Midpoint(A, C_1)
H_3 = Rotate(H_1, -α, O_3)
A_3 = Rotate(A_1, -α, O_3)
C_3 = Rotate(C_1, -α, O_3)
triangleH_3, a_3, h_3, c_3 = Polygon(H_3, C_3, A_3)
δ = Angle(H_3, C, H)
ε = Angle(H, B, H_2)
ζ = Angle(B, A, H)
η = Angle(C, H, A)
θ = Angle(B, A, H_3)
ι = Angle(A, H, B)
γ = Angle(A_2, H_2, B_2)
β = Angle(C_3, H_3, A_3)
κ = Angle(H_2, A, C)