Ermittlung des Anteils der gefärbten
Fläche nur durch Überlegen
(ohne rechnen und messen).

Man dreht die folgenden Flächen um 270°
gegen den Uhrzeigersinn:
A1, B1, I1 (rot)
C1, D1, J1 (blau)
E1, F1, K1 (pink)
G1, H1, L1 (lila)

Hierdurch erhält man fünf gleichgroße Quadrate.
Die grün gefärbte Fläche beträgt somit 1/5 der
gesamten Fläche.

Arbeitsheft Seite 62, Aufgabe 5 b)

A = (-6, 5)
B = (-4, 5)
C = (-2, 5)
E = (-2, 1)
F = (-4, 1)
G = (-6, 1)
H = (-6, 3)
f = Segment(A, C)
g = Segment(C, E)
h = Segment(E, G)
i = Segment(G, A)
k = Segment(C, F)
l = Segment(E, H)
m = Segment(G, B)
K = Intersect(k, l)
L = Intersect(l, m)
A1 = (3, 5)
B1 = (5, 5)
C1 = (7, 5)
D1 = (7, 3)
E1 = (7, 1)
F1 = (5, 1)
G1 = (3, 1)
H1 = (3, 3)
n = Segment(A1, C1)
p = Segment(C1, E1)
q = Segment(E1, G1)
r = Segment(G1, A1)
s = Segment(A1, D1)
t = Segment(C1, F1)
a = Segment(E1, H1)
b = Segment(G1, B1)
I1 = Intersect(s, b)
J1 = Intersect(s, t)
K1 = Intersect(t, a)
L1 = Intersect(a, b)
v2, u, v, w, z_1 = Polygon(I1, J1, K1, L1)
d1, m_1, u_1, n_1 = Polygon(I1, B1, A1)
I1' = Rotate(I1, 270°, A1)
d2, t_1, u', m_2 = Polygon(I1', A1, H1)
d3, p_1, o, v_1 = Polygon(C1, J1, D1)
J1' = Rotate(J1, 270°, C1)
d4, n_2, o_1, v' = Polygon(C1, J1', B1)
K1' = Rotate(K1, 270°, E1)
d5, p_2, w', q_1 = Polygon(K1', E1, D1)
d6, q_2, r_1, w_1 = Polygon(F1, K1, E1)
d7, t_2, s_1, z_2 = Polygon(G1, L1, H1)
L1' = Rotate(L1, 270°, G1)
d8, r_2, s_2, z' = Polygon(G1, L1', F1)
D = Point(g)
j = Segment(A, D)
I = Intersect(m, j)
J = Intersect(k, j)
v1, i_1, j_1, k_1, l_1 = Polygon(I, J, K, L)
A2 = (12, 5)
C2: (16, 5)
E2 = (16, 1)
G2 = (12, 1)
K2': (16.8, 2.6)
J2': (14.4, 5.8)
I2': (11.2, 3.4)
L2': (13.6, 0.2)
c = Segment(G2, J2')
d = Segment(J2', C2)
e = Segment(C2, L2')
f_1 = Segment(L2', G2)
g_1 = Segment(I2', E2)
h_1 = Segment(E2, K2')
a_1 = Segment(K2', A2)
b_1 = Segment(A2, I2')
I2 = Intersect(c, a_1)
L2 = Intersect(c, g_1)
J2 = Intersect(e, a_1)
v4, a2, i2', l2, i2 = Polygon(A2, I2', L2, I2)
v6, j2', c_1, d_1, c2 = Polygon(J2', I2, J2, C2)
Punktv6_1 = PointIn(v6)
Punktv4_1 = PointIn(v4)
K2 = Intersect(e, g_1)
v3, e_1, m_3, l2', g2 = Polygon(L2, K2, L2', G2)
v5, j2, m_4, e2, k2' = Polygon(J2, K2, E2, K2')
v7, f_2, g_2, k2, h_2 = Polygon(I2, J2, K2, L2)
Punktv6 = PointIn(v6)
Punktv4 = PointIn(v4)
Punktv7 = PointIn(v7)
Punktv5 = PointIn(v5)
Punktv3 = PointIn(v3)