pomoćni

\frac{v_a}{2}

v_a

rez na pola visine

\frac{v_a}{2}

drugi rez

a

P\;\; =\;\; a \;\cdot \;\frac{v_a}{\;2\;}

formula

Površina trokuta 

pomoćni 2

\frac{v_a}{2}

pomoćni 3

(šiljastokutnog i tupokutnog)

Antonija Horvatek, lipanj 2010.

α = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
A = (-1.1425961809523815, 4.323703447619053)
trokut2 = 0 (slider from 0 to 2, step 0.1)
C = (5.6771942952380945, 0.08985582857143358)
B = (2.1278609619047613, 0.06450344761905262)
A'_2 = Translate(A, Vector[trokut2 * Vector[B, C]])
C' = Translate(C, Vector[trokut2 * Vector[B, C]])
η: α
B' = Translate(B, Vector[trokut2 * Vector[B, C]])
a = Segment(B, C)
D = Midpoint(a)
b_1 = Line(B, C)
c_1 = OrthogonalLine(A, b_1)
E = Intersect(b_1, c_1)
v_a = Segment(A, E)
e = Segment(E, B)
c = Segment(B, A)
b = Segment(A, C)
F = Midpoint(v_a)
d = OrthogonalLine(F, v_a)
G = Intersect(d, c)
H = Intersect(d, b)
A'_1 = Rotate(A, -(α), H)
G'_1 = Rotate(G, -(α), H)
mnogokut1, g', h, a' = Polygon(H, A'_1, G'_1)
f = OrthogonalLine(B, d)
I = Intersect(d, f)
g = Segment(I, B)
G' = Translate(G, Vector[Vector[B, C]])
mnogokut2, b_2, c_2, g'_1, i = Polygon(B, C, G', I)
j = 0 (slider from 0 to 1, step 0.1)
C'_1 = Dilate(C, j, B)
C''_1 = Translate(C'_1, Vector[Vector[B, I]])
C'' = Translate(C'_1, Vector[Vector[B, G]])
mnogokut3, c'', c', c''_1 = Polygon(C'_1, C''_1, C'')
k = false
mnogokut4, b_3, c_3, h_1, g_1 = Polygon(B, C, H, G)
β = Angle(B, E, A)
J = Midpoint(E, F)
l = Segment(F, E)
m = false
n = Segment(G, H)
K = Midpoint(g)
o = false
γ = Angle(C, B, I)
p = false
q: j
δ: -(η)
N: B'
M: C'
L: A'_2
O, P, Q, R, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, r, s, t, a_1, d_1, e_1, f_1, i_1, j_1, k_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, t_1, a_2, d_2, e_2, f_2, g_2, h_2, mnogokut5, mnogokut6, mnogokut7, mnogokut8, i_2, j_2, ε, ζ = Alat1(L, M, N, δ, q)
u = false
θ = Angle(D_1, M, N)
kutB = Angle(C, B, A)
kutC = Angle(A, C, B)
lij: kutB > 90.0°
des: kutC > 90.0°
F'_1 = Rotate(F, -(α), H)
A'_3 = Rotate(A, -(α), H)
mnogokut9, a'_1, h_3, f' = Polygon(H, F'_1, A'_3)
F' = Rotate(F, α, G)
A' = Rotate(A, α, G)
mnogokut10, q_2, r_2, s_2 = Polygon(G, F', A')
mnogokut11, l_2, m_2, n_2, p_2 = Polygon(B, C, H, G)
k_2 = Segment(C'', H)
v = false
beztupog: (¬lij) ∧ (¬des)

Tool: Alat1
Input: A, B, C, α, j
Output: A', C', C'', C''_1, D, E, F, G, G', G'_1, H, I, J, K, a, a', b, b_1, b_2, b_3, c, c', c'', c''_1, c_1, c_2, c_3, d, e, f, g, g', g'_1, g_1, h, h_1, i, l, mnogokut1, mnogokut2, mnogokut3, mnogokut4, n, v_a, β, γ

a_1 = Segment(B, C)
a = Segment(B, C)
D = Midpoint(a)
b_4 = Line(B, C)
b_1 = Line(B, C)
c_4 = OrthogonalLine(A, b_1)
c_1 = OrthogonalLine(A, b_1)
E_1 = Intersect(b_1, c_1)
E = Intersect(b_1, c_1)
v_1 = Segment(A, E)
v_a = Segment(A, E)
e = Segment(E, B)
c_5 = Segment(B, A)
c = Segment(B, A)
b_5 = Segment(A, C)
b = Segment(A, C)
F_1 = Midpoint(v_a)
F = Midpoint(v_a)
d_1 = OrthogonalLine(F, v_a)
d = OrthogonalLine(F, v_a)
G_1 = Intersect(d, c)
G = Intersect(d, c)
H_1 = Intersect(d, b)
H = Intersect(d, b)
A'_1 = Rotate(A, -(α), H)
A' = Rotate(A, -(α), H)
G'_2 = Rotate(G, -(α), H)
G'_1 = Rotate(G, -(α), H)
mnogokut1_1, g'_2, h_2, a'_1 = Polygon(H, A', G'_1)
mnogokut1, g', h, a' = Polygon(H, A', G'_1)
f = OrthogonalLine(B, d)
I = Intersect(d, f)
g = Segment(I, B)
G' = Translate(G, Vector[Vector[B, C]])
mnogokut2, b_2, c_2, g'_1, i = Polygon(B, C, G', I)
C' = Dilate(C, j, B)
C''_1 = Translate(C', Vector[Vector[B, I]])
C'' = Translate(C', Vector[Vector[B, G]])
mnogokut3_1, c''_2, c'_1, c''_3 = Polygon(C', C''_1, C'')
mnogokut3, c'', c', c''_1 = Polygon(C', C''_1, C'')
mnogokut4_1, b_6, c_6, h_3, g_2 = Polygon(B, C, H, G)
mnogokut4, b_3, c_3, h_1, g_1 = Polygon(B, C, H, G)
β = Angle(B, E, A)
J = Midpoint(E, F)
l = Segment(F, E)
n = Segment(G, H)
K = Midpoint(g)
γ = Angle(C, B, I)