A

a

c

a

b

d

h

A

c

A

h

c|A(c)

h|A(h)

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

Flächeninhaltsformeln

(a|A)

A(a)

A(c)

(c|A)

A(h)

(h|A)

Koordinatendarstellung

Tabellendarstellung

a|A(a)

Δx = 0.5 (slider from 0.1 to 1, step 0.1)
h = 1.5 (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)
B1 = (-8.24, 9.475248618784528)
A = (-5.48, 0.7152486187845284)
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)
A1 = Midpoint(W, E)
f1 = Segment(V, W)
g1 = Segment(W, E)
T13: " \fgcolor{000000}{  \fbox{ \begin{tabular} {|r|c|r}
\fgcolor{0000FF}{c} & | & \fgcolor{0000FF}{A(c)} \\  " + (c - 4 Δx) + " & | & " + ((c - 4 Δx + a) / 2 h) + "\\ " + (c - 3 Δx) + " &| & " + ((c - 3 Δx + a) / 2 h) + "\\ " + (c - 2 Δx) + " &| & " + ((c - 2 Δx + a) / 2 h) + "\\ " + (c - Δx) + " &| & " + ((c - Δx + a) / 2 h) + "\\ \fgcolor{0000FF}{" + c + "} &| & \fgcolor{0000FF}{" + ((c + a) / 2 h) + "}\\ " + (c + Δx) + " &| & " + ((c + Δx + a) / 2 h) + "\\ " + (c + 2 Δx) + " &| & " + ((c + 2 Δx + a) / 2 h) + "\\ " + (c + 3 Δx) + " &| & " + ((c + 3 Δx + a) / 2 h) + "\\ " + (c + 4 Δx) + " &| & " + ((c + 4 Δx + a) / 2 h) + "\\ 
\end{tabular} }} "
T14: " \fgcolor{000000}{  \fbox{ \begin{tabular} {|r|c|r}
\fgcolor{00FF00}{h} & | & \fgcolor{00FF00}{A(h)} \\  " + (h - 4 Δx) + " & | & " + ((a + c) / 2 * (h - 4 Δx)) + "\\ " + (h - 3 Δx) + " &| & " + ((a + c) / 2 * (h - 3 Δx)) + "\\ " + (h - 2 Δx) + " &| & " + ((a + c) / 2 * (h - 2 Δx)) + "\\ " + (h - 1 Δx) + " &| & " + ((a + c) / 2 * (h - 1 Δx)) + "\\ \fgcolor{00FF00}{" + h + "} &| & \fgcolor{00FF00}{" + ((a + c) / 2 h) + "}\\ " + (h + 1 Δx) + " &| & " + ((a + c) / 2 * (h + 1 Δx)) + "\\ " + (h + 2 Δx) + " &| & " + ((a + c) / 2 * (h + 2 Δx)) + "\\ " + (h + 3 Δx) + " &| & " + ((a + c) / 2 * (h + 3 Δx)) + "\\ " + (h + 4 Δx) + " &| & " + ((a + c) / 2 * (h + 4 Δx)) + "\\ 
\end{tabular} }} "
i1 = false
j1 = false
D1: (x(B1) + 4, y(B1) - 1.3)
E1: (x(B1) + 4, y(B1))
C1: (x(B1), y(B1) - 1.3)
poly1, l1, m1, n1, p1 = Polygon(B1, C1, D1, E1)
G1: (x(B1), y(B1) - 2.4)
F1: (x(B1), y(B1) - 1.5)
H1: (x(B1) + 4, y(B1) - 2.4)
I1: (x(B1) + 4, y(B1) - 1.5)
poly2, q1, r1, s1, t1 = Polygon(F1, G1, H1, I1)
poly3, a2, b2, c2 = Polygon(A, C, D)
J1: (0, poly3)
poly4, d2, e2, f2 = Polygon(A, B, C)
K1: (0, poly4)
γ = Angle(L, M, C)
o1 = false
k1 = false
u1 = false
v1 = false
w1 = false
z1 = false
g2 = false
h2 = false
L1: (x(B1) + 4.2, y(B1))
M1: (x(B1) + 7.8, y(B1))
N1: (x(B1) + 7.8, y(B1) - 2.4)
O1: (x(B1) + 4.2, y(B1) - 2.4)
poly5, i2, j2, k2, l2 = Polygon(L1, O1, N1, M1)
T23: "A_{grau} = " + A_{Trapez}
P1: (x(B1), y(B1) - 2.6)
Q1: (x(B1), y(B1) - 5.6)
R1: (x(B1) + 2, y(B1) - 5.6)
S1: (x(B1) + 2, y(B1) - 2.6)
poly6, m2, n2, p2, q2 = Polygon(P1, Q1, R1, S1)
r2 = Ray(J1, G)
o2 = false
s2 = Ray(K1, I)
o = false
u = false
t2 = false
a3 = Ray(E, V)
v = false
u2 = false
w = false
T12: " \fgcolor{000000}{  \fbox{ \begin{tabular} {|r|c|r}
\fgcolor{FF0000}{a} & | & \fgcolor{FF0000}{A(a)} \\  " + (a - 4 Δx) + " & | & " + ((a - 4 Δx + c) / 2 h) + "\\ " + (a - 3 Δx) + " &| & " + ((a - 3 Δx + c) / 2 h) + "\\ " + (a - 2 Δx) + " &| & " + ((a - 2 Δx + c) / 2 h) + "\\ " + (a - Δx) + " &| & " + ((a - Δx + c) / 2 h) + "\\ \fgcolor{FF0000}{" + a + "} &| & \fgcolor{FF0000}{" + ((a + c) / 2 h) + "}\\ " + (a + Δx) + " &| & " + ((a + Δx + c) / 2 h) + "\\ " + (a + 2 Δx) + " &| & " + ((a + 2 Δx + c) / 2 h) + "\\ " + (a + 3 Δx) + " &| & " + ((a + 3 Δx + c) / 2 h) + "\\ " + (a + 4 Δx) + " &| & " + ((a + 4 Δx + c) / 2 h) + "\\ 
\end{tabular} }} "
h1 = false
z = false