Author: P.Goubet

Aire d'un losange

Utiliser les curseurs pour construire le rectangle H_2H_3H_4H_5

L'aire du rectangle H_2H_3H_4H_5 est :

L'aire du losange ABCD est :

\frac{diagonale1 x diagonale2}{2} 

H_5H_4 x H_2H_5  =  AC x BD

 \frac{AC x BD}{2}  =

k_1 = 2.1 (slider from 1 to 2.5, step 0.1)
A: (-k_1, 0)
k_2 = 0.8 (slider from 0.5 to 1.5, step 0.1)
B: (0, k_2)
C: (k_1, 0)
D: (0, -k_2)
AC = Segment(A, C)
BD = Segment(B, D)
losangeABCD, AB, BC, CD, AD = Polygon(A, B, C, D)
H = Intersect(AC, BD)
U = (-3, -2)
t = 0 (slider from 0 to 5, step 0.1)
V: (t - 3, -2)
u = Vector(U, V)
A_1 = Translate(A, u)
B_1 = Translate(B, u)
H_1 = Translate(H, u)
translatéAHB, b_1, a_1, h_1 = Polygon(A_1, H_1, B_1)
τ = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
O_2 = Midpoint(B, A_1)
A_2 = Rotate(A_1, τ, O_2)
B_2 = Rotate(B_1, τ, O_2)
H_2 = Rotate(H_1, τ, O_2)
triangleH_2, e, f, g = Polygon(B_2, H_2, A_2)
C_1 = Translate(C, u)
D_1 = Translate(D, u)
translatéBHC, h_2, b_2, c_1 = Polygon(B_1, C_1, H_1)
O_3 = Midpoint(B_1, C)
C_3 = Rotate(C_1, τ, O_3)
B_3 = Rotate(B_1, τ, O_3)
H_3 = Rotate(H_1, τ, O_3)
triangleH_3, f_1, e_1, g_1 = Polygon(C_3, H_3, B_3)
translatéCHD, d_1, h_3, c_2 = Polygon(H_1, C_1, D_1)
translatéAHD, d_2, a_2, h_5 = Polygon(A_1, H_1, D_1)
B_2' = Mirror(B_2, AC)
H_5 = Mirror(H_2, AC)
A_2' = Mirror(A_2, AC)
triangleH_5, a_2', b_2', h_2' = Polygon(B_2', H_5, A_2')
C_3' = Mirror(C_3, AC)
H_4 = Mirror(H_3, AC)
B_3' = Mirror(B_3, AC)
triangleH_4, b_3', c_3', h_3' = Polygon(C_3', H_4, B_3')
α = Angle(B_2, H_2, A_2)
β = Angle(C_3, H_3, B_3)
γ = Angle(B_3', H_4, C_3')
δ = Angle(A_2', H_5, B_2')
ε = Angle(B, H, A)
ζ = Angle(B_1, H_1, A_1)