trapezflaeche_funktional

A_{Trapez}=\frac{a+c}{2} \cdot h

A_{Parallelogramm}=a \cdot h_a

A_{Dreieck}=\frac{1}{2} \cdot g \cdot h

A_{Rechteck}=a \cdot b

A_{Quadrat}=a^{2}

= \frac{1}{2} \cdot a \cdot h + \frac{1}{2} \cdot c \cdot h

= \frac{h}{2} \cdot a +  \frac{h}{2} \cdot c

Dreieck

Trapez

Parallelogramm

1

2

Rechteck

Quadrat

Flächeninhalt

(a|A)

A(a)

A(c)

(c|A)

A(h)

(h|A)

Koordinatendarstellung

x( G )

y( G )

h = 1.6 (slider from 0 to 8, step 0.1)
c = 2 (slider from 0 to 8, step 0.1)
a = 4 (slider from 0 to 8, step 0.1)
B_1 = (-8.24, 9.475248618784528)
A = (-6.48, 0.915248618784523)
b = Line(A, xAxis)
d = Circle(A, a)
B = Intersect(d, b, 2)
e = OrthogonalLine(A, b)
f = Circle(A, h)
H = Intersect(f, e, 2)
g = Line(H, b)
C = Point(g)
k = Circle(C, c)
D = Intersect(k, g, 1)
A_{Trapez}, i, j, l, m = Polygon(A, B, C, D)
E = Intersect(xAxis, yAxis)
p = Circle(E, a)
F = Intersect(p, xAxis, 2)
n = OrthogonalLine(F, xAxis)
q = Circle(F, A_{Trapez})
G = Intersect(q, n, 2)
I: (c, A_{Trapez})
r = Segment(E, F)
J = Midpoint(E, F)
s = Segment(F, G)
K = Midpoint(G, F)
L = Point(b)
t = OrthogonalLine(L, b)
M = Intersect(g, t)
a1 = Segment(M, L)
b1 = Segment(D, M)
N: (c, 0)
c1 = Segment(I, N)
d1 = Segment(E, N)
O = Midpoint(D, C)
P = Midpoint(M, L)
Q = Midpoint(A, B)
R = Midpoint(B, C)
S = Midpoint(A, D)
β = Angle(M, L, A)
T = Midpoint(E, N)
U = Midpoint(I, N)
e1 = Segment(A, L)
V: (h, A_{Trapez})
W: (h, 0)
Z = Midpoint(V, W)
A_1 = Midpoint(W, E)
f1 = Segment(V, W)
g1 = Segment(W, E)
D_1: (x(B_1) + 4, y(B_1) - 1.3)
E_1: (x(B_1) + 4, y(B_1))
C_1: (x(B_1), y(B_1) - 1.3)
poly1, l1, m1, n1, p1 = Polygon(B_1, C_1, D_1, E_1)
G_1: (x(B_1), y(B_1) - 2.4)
F_1: (x(B_1), y(B_1) - 1.5)
H_1: (x(B_1) + 4, y(B_1) - 2.4)
I_1: (x(B_1) + 4, y(B_1) - 1.5)
poly3, a2, b2, c2 = Polygon(A, C, D)
J_1: (0, poly3)
poly4, d2, e2, f2 = Polygon(A, B, C)
K_1: (0, poly4)
γ = Angle(L, M, C)
o1 = false
k1 = false
u1 = false
v1 = false
w1 = false
z1 = false
g2 = false
h2 = false
L_1: (x(B_1) + 4.2, y(B_1))
M_1: (x(B_1) + 7.8, y(B_1))
N_1: (x(B_1) + 7.8, y(B_1) - 2.4)
O_1: (x(B_1) + 4.2, y(B_1) - 2.4)
poly5, i2, j2, k2, l2 = Polygon(L_1, O_1, N_1, M_1)
T23: "A_{grau} = " + A_{Trapez}
P_1: (x(B_1), y(B_1) - 1.6)
Q_1: (x(B_1), y(B_1) - 4.6)
R_1: (x(B_1) + 2, y(B_1) - 4.6)
S_1: (x(B_1) + 2, y(B_1) - 1.6)
poly6, m2, n2, p2, q2 = Polygon(P_1, Q_1, R_1, S_1)
r2 = Ray(J_1, G)
o2 = false
s2 = Ray(K_1, I)
o = false
u = false
t2 = false
a3 = Ray(E, V)
v = false
u2 = false
w = false
U2 = 8
V2 = 7.5
U3 = 7
V3 = 6.749999999999999
U4 = 6
V4 = 6
U5 = 5
V5 = 5.249999999999999
U6 = 4
V6 = 4.499999999999999
U7 = 3
V7 = 3.749999999999999
U8 = 2
V8 = 2.999999999999999
U9 = 1
V9 = 2.249999999999999
U10 = 0
V10 = 1.4999999999999991