Rectángulo

Romboide

Triángulo

Trapecio

Cuadrilátero

Polígono regular

Recomponer

Área

Número de lados

Apotema

A

B

C

D

E

y3 = 2.22 (slider from -1 to 3, step 0.01)
x3 = 10.94 (slider from 7 to 11, step 0.01)
E3: (x3, y3)
y2 = -2 (slider from -3 to -2, step 0.01)
x2 = 8 (slider from 7 to 10, step 0.01)
E2: (x2, y2)
y1 = -2 (slider from -3 to -1, step 0.01)
x1 = 4 (slider from 3 to 6, step 0.01)
E1: (x1, y1)
i_5 = Line(E3, Line[E1, E2])
C = Intersect(Line[(6, 0), (6, 1)], i_5)
C' = Intersect(Line[(5, 0), (5, 1)], i_5)
E4 = Point(Segment[C, C'])
E4': E4 - (0.2, 1.5)
c4, e1_3, e2_1, e3_2, e4' = Polygon(E1, E2, E3, E4')
E3' = Mirror(E3, C)
transf = 0 (slider from 0 to 2, step 0.1)
nlados = 6 (slider from 3 to 12, step 1)
Bpr = (0, -3)
Apr = (8, 2)
z1 = 5 (slider from 0 to 5, step 1)
N10: E1 - (0, 1)
Esquina2rectangulo: (x(E3), y(E1))
c = Segment(E2, E1)
E4ro = Intersect(Line[E1, Line[E2, E3]], Line[E3, c])
ro1, a_4, e, d_4, c_3 = Polygon(E1, E4ro, E3, E2)
B1 = Intersect(OrthogonalLine[E1, d_4], d_4)
B2 = Intersect(OrthogonalLine[E4ro, d_4], d_4)
B3 = Intersect(OrthogonalLine[E2, e], e)
B4 = Intersect(OrthogonalLine[E1, e], e)
B5 = If((AffineRatio[E2, E3, B1] ≥ 0) ∧ (AffineRatio[E2, E3, B1] ≤ 1), B1, If[(AffineRatio[E2, E3, B2] ≥ 0) ∧ (AffineRatio[E2, E3, B2] ≤ 1), B2, If[(AffineRatio[E4ro, E3, B3] ≥ 0) ∧ (AffineRatio[E4ro, E3, B3] ≤ 1), B3, B4]])
u1 = Vector(E2, B5)
r2 = 0 (slider from 0 to 1, step 0.1)
w = UnitOrthogonalVector(Vector[E4ro, E1])
ww = UnitVector(Vector[E1, E4ro])
H: E4ro + ((1 - r2) * (E1 - E4ro))
a: y = y(E1)
g = OrthogonalLine(E4ro, a)
B5a: B5 + ((B2 - B5) * r2)
Ga: E3 + H - E4ro
B = (-2, 4)
Ea: E4ro + H - E4ro
b: y = y(B)
f = OrthogonalLine(E1, a)
ro2, b_2, h_2, i_2 = Polygon(B5a, Ga, Ea)
ro3, a_2, c_2, e_2, g_2 = Polygon(E4ro, E1, B5, E3)
v1 = Vector(E4ro, H)
D' = Translate(E3, v1)
M1: E4ro + ww
M2: E3 + ww + If[B5 ≟ B1, u1, E2 - E3 + u1]
N1: E1 + w
N2: E4ro + w
F = Intersect(b, f)
listaromboide: {x(E3), x(E4ro)}
cota1 = Segment(M1, M2)
z_1: 7 - z1
j = Segment(N1, N2)
Esquina4rectangulo: (x(E1), y(E3))
polígono1, esquina1, esquina2rectangulo, esquina3, esquina4rectangulo = Polygon(E1, Esquina2rectangulo, E3, Esquina4rectangulo)
hrec = Segment(Esquina2rectangulo, Esquina2rectangulo + (0, (-1.2)))
N11: Esquina2rectangulo + N10 - E1
E4tri: E2
triangulo1, esquina3_1, esquina1_1, esquina2triangulo = Polygon(E1, E4tri, E3)
A = Midpoint(esquina2triangulo)
α1 = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
Esquina1'_1 = Rotate(E1, α1, A)
Esquina2triangulo'_1 = Rotate(E4tri, α1, A)
Esquina3'_1 = Rotate(E3, α1, A)
polígono3, esquina2triangulo', esquina3', esquina1' = Polygon(Esquina3'_1, Esquina1'_1, Esquina2triangulo'_1)
l = OrthogonalLine(E3, a)
D = Intersect(Line[E1, E1 + E3 - E2], OrthogonalLine[E3, Line[E2, E3]])
m = Segment(E3, D)
E = Midpoint(m)
N1t: E2 - UnitOrthogonalVector[Vector[E2, E3]]
hrec1 = Segment(E1, E1 + (0, (-1.2)))
q = Segment(E3, E3 + (1.2, 0))
q2 = Segment(Esquina2rectangulo, Esquina2rectangulo + (1.2, 0))
T41: Esquina2rectangulo + (1, 0)
T42: E3 + (1, 0)
r = Segment(T42, T41)
J = Midpoint(r)
E4tra: E2
trapecio, esquina1_2, esquina2trapecio, esquina3_2, esquina4trapecio = Polygon(E1, E4tra, E3, E4)
K = Midpoint(esquina2trapecio)
polígono6, esquina4trapecio_1, k_1, esquina3_3 = Polygon(K, E3, E4)
α2 = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
Esquina3'_3 = Rotate(E3, (-α2), K)
Esquina4trapecio' = Rotate(E4, (-α2), K)
triangulotrapecio2, esquina4trapecio', k_2, esquina3'_2 = Polygon(K, Esquina3'_3, Esquina4trapecio')
cuadrilaterotrapecio, esquina1_3, esquina2trapecio_1, k_3, esquina4trapecio_2 = Polygon(E1, E4tra, K, E4)
Cotatrap1: E1 + UnitOrthogonalVector[Vector[E2, E1]]
Cotatrap3: Esquina4trapecio' + UnitOrthogonalVector[Vector[E2, E1]]
b_1 = OrthogonalLine(E4, a)
L = Intersect(OrthogonalLine[E4, Line[E1, E2]], Line[E1, E2])
h_1 = Segment(E4, L)
texto4: "b = " + (x(Esquina2rectangulo) - x(E1)) + " cm"
texto15: "h = " + (y(E3) - y(E1)) + " cm"
Esquina4cuad: E4'
O = Midpoint(e4')
P = Midpoint(e3_2)
R = Midpoint(e1_3)
Q = Midpoint(e2_1)
Esquina2cuad: E2
α3 = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
O'_1 = Rotate(O, α3, R)
Esquina1' = Rotate(E1, α3, R)
polígono5, esquina1'_2, r_2, o' = Polygon(R, O'_1, Esquina1')
P'_1 = Rotate(P, (-α3), Q)
N' = Rotate(E3, (-α3), Q)
polígono7, n', q_2, p' = Polygon(Q, P'_1, N')
j_1 = Segment(E3, Esquina2cuad)
Pcuad: E4' + (α3 / 3.141592653589793 * (E2 - E4'))
u = Vector(E4', Pcuad)
Esquina3' = Translate(E4', u)
P' = Translate(P, u)
O' = Translate(O, u)
polígono8, esquina3'_3, o'_1, p'_1 = Polygon(O', P', Esquina3')
polígono9, m_2, r_3, q_3 = Polygon(R, Q, Esquina2cuad)
polígono10, r_4, esquina2cuad, q_4, p_2, o_1 = Polygon(R, Esquina2cuad, Q, P, O)
M = Midpoint(O, P)
Z = Intersect(Line[Q, R], OrthogonalLine[M, Line[Q, R]])
s_1 = Segment(M, Z)
A_1 = Midpoint(s_1)
texto20: "h = " + (Distance[M, Z])
texto21: "b = " + (Distance[O, P])
texto23: "Área = b x h = " + (x(Esquina2rectangulo) - x(E1)) + " x " + (y(E3) - y(E1)) + " = " + polígono1 + " cm²"
v = false
listacuad1 = Sequence(Segment[(-1, s), (15, s)], s, -5, 5)
listacuad2 = Sequence(Segment[(t, (-5)), (t, 5)], t, -1, 15)
anclalogo = (-3.8000000000000003, -4.94)
i = Segment(E4ro, E4ro + (1.2 * w))
h = Segment(E1, E1 + (1.2 * w))
h1 = Segment(E4ro, E4ro + (1.2 * ww))
B5b: B5 + ((B1 - B5) * r2)
Gb: E4ro + ((B1 - B5) * r2)
Eb: E3 + ((B1 - B5) * r2)
ro2', e'', b3'', g'' = Polygon(B5b, Gb, Eb)
ro3', esquina2romboide, esquina1_5, esquina4romboide, b3 = Polygon(E4ro, E1, E2, B5)
texto1: "h = " + cota1 + " cm"
texto2: "b = " + j + " cm"
h2 = Segment(E3, E3 + (1.2 * ww) + If[B5 ≟ B1, u1, E2 - E3 + u1])
B5c: B5 + ((B4 - B5) * r2)
Ec: E3 + ((B4 - B5) * r2)
Gc: E2 + ((B4 - B5) * r2)
ro4, b5c, gc, ec = Polygon(Gc, Ec, B5c)
ro4', e1, e2ro, b5, e4ro = Polygon(E1, E4ro, B5, E2)
N1c: E1 + UnitVector[Vector[B5, E4ro]]
N2c: E4ro + UnitVector[Vector[B5, E4ro]] + If[B5 ≟ B3, B5 - E3, B3 - E3]
hc = Segment(E1, E1 + (1.2 * UnitVector[Vector[B5, E4ro]]))
d = Segment(N1c, N2c)
texto25: "b = " + d + " cm"
M1c: B3 + UnitVector[Vector[E2, B3]]
M2c: E1 + M1c - E2
c_1 = Segment(E1, E1 + B3 - E2 + (1.2 * UnitVector[Vector[E2, B3]]))
d_1 = Segment(M1c, M2c)
texto26: "h = " + d_1 + " cm"
k = Segment(N10, N11)
B5d: B5 + ((B3 - B5) * r2)
Ed: E1 + ((B3 - B5) * r2)
Gd: E4ro + ((B3 - B5) * r2)
ro5', gd, ed, b5d = Polygon(Ed, B5d, Gd)
ro5, e3, e4ro_1, e1_1, b4 = Polygon(E3, E2, E1, B4)
ic = Segment(E4ro, E4ro + If[B5 ≟ B3, B5 - E3, B3 - E3] + (1.2 * UnitVector[Vector[B5, E4ro]]))
a_1 = Segment(E2, B3 + (1.2 * UnitVector[Vector[E2, B3]]))
poli1A, g_1, t_1, d_2, f_2, j_2, l_2, n_2, s_2, t_2, a_3 = Polygon((0, 5), (0, 2), (1, 2), (1, 1), (5, 1), (5, 2), (2, 2), (2, 3), (1, 3), (1, 5))
poli1C, b_3, d_3, e_3, f_3 = Polygon((0, 0), (0, -2), (4, -2), (4, 0))
poli1B, s_3, t_3, b_4, c_4, e_4, f_4, g_4, h_4 = Polygon((8, 4), (8, 3), (9, 3), (9, 0), (13, 0), (13, 3), (11, 3), (11, 4))
poli1D, g_3, h_3, i_3, j_3, l_3, m_3, n_3, p_3 = Polygon((0, -4), (3, -4), (3, -5), (7, -5), (7, -4), (4, -4), (4, -3), (0, -3))
poli1E, i_4, j_4, k_4, l_4, m_4, n_4, p_4, s_4, t_4, a_5, b_5, c_5, d_5, e_5, f_5, g_5 = Polygon((7, -1), (7, -2), (6, -2), (6, -3), (8, -3), (8, -2), (10, -2), (10, -5), (11, -5), (11, -2), (12, -2), (12, -4), (14, -4), (14, -2), (13, -2), (13, -1))
texto3: "Área = b x h = " + (If[B5 ≟ B1 ∨ B5 ≟ B2, round((100 * j)) / 100 + " x " + (round((100 * cota1)) / 100) + " = " + ((round((100 * j)) / 100 * round((100 * cota1)) / 100)) + " cm²", round((100 * d)) / 100 + " x " + (round((100 * d_1)) / 100) + " = " + ((round((100 * d)) / 100 * round((100 * d_1)) / 100)) + " cm²"])
N0t: E3 - UnitOrthogonalVector[Vector[E2, E3]]
p = Segment(N0t, N1t)
r1 = 2.2 (slider from 0 to 4, step 0.1)
Lverp = Sequence((x(Apr) + (r1 * cos(t)), y(Apr) + (r1 * sin(t))), t, 0°, 360°, (360 / nlados)°)
Mapotema: (Element[Lverp, 1] + Element[Lverp, 2]) / 2
lado = Distance(Element[Lverp, 1], Element[Lverp, 2])
texto30: "Perímetro = " + nlados + " x " + lado + " = " + ((nlados * lado)) + " cm"
apotema: sqrt(r1^(2) - (lado / 2)^(2))
texto28: "Apotema = " + apotema + " cm"
texto31: "Área \;  =  \;  \frac{ perímetro \;  x \;  apotema }{ 2} = \frac{ " + nlados + " \;   x \;   " + lado + " \;   x \;  " + apotema + " }{ 2} \; = \;" + (((nlados * lado) * apotema / 2)) + " \; cm²"
Lvert1 = Sequence(Bpr + ((lado * t), 0), t, 0, nlados)
Ctapr1: Bpr + (0, -1)
Ctapr2: Bpr + ((nlados * lado), -1)
Ctapr3: Bpr + ((nlados * lado) + 1, 0)
Ctapr4: Bpr + ((nlados * lado) + 1, apotema)
e_1 = Segment(Ctapr1, Ctapr2)
f_1 = Segment(Ctapr3, Ctapr4)
Llados = Sequence(Polygon[Element[Lverp, t], Element[Lverp, t + 1], Apr], t, 1, nlados)
Langu = Sequence(Angle[Element[Lverp, t] + (1, 0), Element[Lverp, t], Element[Lverp, t + 1]], t, 1, nlados)
Lpuntosrot1 = Sequence(Element[Lverp, t] + ((transf - 1) * (Element[Lvert1, t] - Element[Lverp, t])), t, 1, nlados + 1)
Lvert2 = Sequence(Bpr + ((lado * t) - lado / 2, apotema), t, 1, nlados)
Lpuntosrot2 = Sequence(Apr + ((transf - 1) * (Element[Lvert2, t] - Apr)), t, 1, nlados)
Lrot0 = Sequence(Rotate[Element[Lverp, t + 1], ((-transf) * Element[Langu, t]), Element[Lverp, t]], t, 1, nlados)
Lrot1 = Sequence(Rotate[Apr, ((-transf) * Element[Langu, t]), Element[Lverp, t]], t, 1, nlados)
Ltrianrot0 = Sequence(Polygon[Element[Lverp, t], Element[Lrot0, t], Element[Lrot1, t]], t, 1, nlados)
Ltrianrot1 = Sequence(Polygon[Element[Lpuntosrot1, t], Element[Lpuntosrot1, t] + (lado, 0), Element[Lpuntosrot1, t] + (lado / 2, apotema)], t, 1, nlados)
Ltrianrot2 = Sequence(Polygon[Element[Lvert2, t], Element[Lvert2, t] + (lado, 0), Element[Lvert1, t + 1]], t, 1, nlados)
cotapr10 = Segment(Bpr, Bpr + (0, (-1.2)))
cotapr11 = Segment(Bpr + ((nlados * lado), 0), Bpr + ((nlados * lado), (-1.2)))
cotapr20 = Segment(Bpr + ((nlados * lado), 0), Bpr + ((nlados * lado) + 1.2, 0))
cotapr210 = Segment(Element[Lvert2, nlados], Bpr + ((nlados * lado), apotema))
cotapr211 = Segment(Bpr + ((nlados * lado), apotema), Bpr + ((nlados * lado) + 1.2, apotema))
apote = Segment(Apr, Mapotema)
h_5 = Segment(B5a, B5a + (1.2 * ww))
htr0 = Segment(E3, E3 - (1.2 * UnitOrthogonalVector[Vector[E2, E3]]))
htr = Segment(E4tri, E4tri - UnitOrthogonalVector[Vector[E2, E3]])
s1trap = Segment(E1, E1 + (1.2 * UnitOrthogonalVector[Vector[E2, E1]]))
s3trap = Segment(Esquina4trapecio', Esquina4trapecio' + (1.2 * UnitOrthogonalVector[Vector[E2, E1]]))
i_1 = Segment(E1, L)
t = Segment(E2, E2 + (1.2 * UnitOrthogonalVector[Vector[E2, E1]]))
Cotatrap2: E2 + UnitOrthogonalVector[Vector[E2, E1]]
j_5 = Segment(Cotatrap1, Cotatrap2)
texto17: "B = " + j_5 + " cm"
s = Segment(Cotatrap2, Cotatrap3)
texto16: "b = " + s + " cm"
texto18: "h = " + h_1 + " cm"
texto19: "Área  \; = \;   \frac{( B+b) \; x \;  h }{2 } \; = \;  \frac{( " + (round((100 * j_5)) / 100) + "+" + (round((100 * s)) / 100) + " )\; x \; " + (round((100 * h_1)) / 100) + " }{ 2} \; = \; " + (((round((100 * j_5)) / 100 + round((100 * s)) / 100) * round((100 * h_1)) / 200)) + " \; cm²"
polígono2, r_1, o, p_1, q_1 = Polygon(R, O, P, Q)
texto22: "Área = 2 x b x h = 2 x " + (round((100 * Distance[O, P])) / 100) + " x " + (round((100 * Distance[Z, M])) / 100) + " = " + ((round((100 * Distance[O, P])) / 50 * round((100 * Distance[Z, M])) / 100)) + " cm²"
n = Segment(E1, D)
texto13: "h = " + (Distance[D, E3]) + " cm"
texto14: "b = " + (Distance[E2, E3]) + " cm"
texto24: "Área \; = \;  \frac{ b \;  x  \; h }{2 } \; =  \;  \frac{ " + (Distance[E2, E3]) + " \; x \; " + (Distance[D, E3]) + " }{ 2} \; = \; " + triangulo1 + " \; cm²"
Llados2 = Sequence(Polygon[Element[Lverp, t], Element[Lverp, t + 1], Apr], t, 1, nlados)