Animation

Grande Diagonale

Petite Diagonale

Aire d'un losange

Aire du losange = Aire du rectangle : 2
Aire du rectangle = Grande Diagonale x Petite Diagonale

Aire du losange = (Grande Diagonale x Petite Diagonale) : 2

α = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
O = Intersect(xAxis, yAxis)
B = Point(xAxis)
C = Point(yAxis)
D = Mirror(B, O)
A = Mirror(C, O)
a = Segment(B, D)
b = Segment(A, C)
poly1, c, b_1, a_1 = Polygon(B, O, C)
B'_2 = Mirror(B, O)
A'_1 = Mirror(O, O)
C'_2 = Mirror(C, O)
poly1'_1, c', b', a' = Polygon(B'_2, A'_1, C'_2)
B'_3 = Mirror(B, yAxis)
A'_2 = Mirror(O, yAxis)
C'_3 = Mirror(C, yAxis)
poly1'_2, c'_1, b'_1, a'_1 = Polygon(B'_3, A'_2, C'_3)
B'_4 = Mirror(B, xAxis)
A'_3 = Mirror(O, xAxis)
C'_4 = Mirror(C, xAxis)
poly1'_3, c'_2, b'_2, a'_2 = Polygon(B'_4, A'_3, C'_4)
D_1 = Midpoint(a_1)
E_1 = Midpoint(a'_1)
F_1 = Midpoint(a')
G_1 = Midpoint(a'_2)
B' = Rotate(B, -(α), D_1)
F = Rotate(O, -(α), D_1)
C' = Rotate(C, -(α), D_1)
poly1', c'_3, b'_3, a'_3 = Polygon(B', F, C')
H_1 = Rotate(B'_4, α, G_1)
E = Rotate(A'_3, α, G_1)
J = Rotate(C'_4, α, G_1)
poly2, j, h, i = Polygon(H_1, E, J)
K = Rotate(B'_2, -(α), F_1)
H = Rotate(A'_1, -(α), F_1)
M = Rotate(C'_2, -(α), F_1)
poly3, m, k, l = Polygon(K, H, M)
N = Rotate(B'_3, α, E_1)
G = Rotate(A'_2, α, E_1)
P = Rotate(C'_3, α, E_1)
poly4, p, n, o = Polygon(N, G, P)