Arc AC = 

Arc CD =

Arc DE =

Arc EB =

\frac{2·\pi·2,4}{3} = 1,6\pi ≈ 5,03 cm 

\frac{2·\pi·4,8}{3} = 3,2\pi ≈10,05 cm 

\frac{2·\pi·7,2}{3} = 4,8\pi≈15,08 cm 

\frac{2·\pi·9,6}{3} =6,4\pi≈ 20,11 cm 

2,4

4,8

7,2

9,6

Longueur totale =

1,6\pi+3,2\pi+4,8\pi+6,4\pi=16\pi

≈50,27 cm

a) Longueur spirale AB

Réponses

b) Surface bleue

Secteur OBE

Secteur AED

Secteur MDC

Triangle AMO

:\frac{\pi·9,6^2}{3}≈96,51 cm^2

:\frac{\pi·7,2^2}{3}≈54,29 cm^2

:\frac{\pi·4,8^2}{3}≈24,13 cm^2

h:\sqrt{2,4^2-1,2^2}≈2,08cm

h

Aire :\frac{2,4·2,08}{2}≈2,49 cm^2

Surface totale

96,51+54,29+24,13+2,49≈177,42cm^2

A = (1.0582163716456892, -0.16078731198868226)
M = (0, -2)
a = Segment(A, M)
poly1, b, c, d, O = Polygon(A, M, 3)
e = Ray(O, A)
f = Ray(A, M)
g = Ray(M, O)
h = Circle(O, A)
C = Intersect(h, g, 2)
k = CircleArc(O, C, A)
p = Circle(M, C)
D = Intersect(p, f, 1)
q = CircleArc(M, D, C)
r = Circle(A, D)
E = Intersect(r, e, 1)
s = CircleArc(A, E, D)
t = Circle(O, E)
B = Intersect(t, g, 1)
c_1 = CircleArc(O, B, E)
F = Point(k)
i = Segment(O, F)
G = Midpoint(i)
j = false
H = Point(q)
l = Segment(M, H)
I = Midpoint(l)
m = false
J = Point(s)
n = Segment(J, A)
K = Midpoint(n)
o = false
L = Point(c_1)
a_1 = Segment(L, O)
M_1 = Midpoint(a_1)
u = false
v = false
w = true
z = false
b_1 = false
d_1 = CircleSector(O, B, E)
e_1 = false
f_1 = CircleSector(A, E, D)
g_1 = false
h_1 = CircleSector(M, D, C)
i_1 = false
poly2, a_2, o_1, m_1 = Polygon(O, M, A)
j_1 = false
k_1 = OrthogonalLine(A, g)
N = Intersect(k_1, a_2)
l_1 = Segment(A, N)
n_1 = false
P = Point(g)
p_1 = Segment(M, P)