choose a figure

45 cm²

25 cm²

20 cm²

9 cm²

A

B

C

D

E

F

35 cm²

22cm²

15 cm²

24 cm²

48 cm²

60 cm²

36 cm²

42 cm²

14 cm²

s_4: sqrt(36 - 4.8^(2))
b_3: (2 * sqrt(7) / 3^(0.25))
s_3: 28 / b_3
s'_3: sqrt(s_3^(2) + b_3^(2) / 4)
b_1: 5
a, A, B, C, face1, face2, face3, face4, face5, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8 = Prism(Polygon[(((-b_1)) / 2, ((-b_1)) / 2), (b_1 / 2, ((-b_1)) / 2), 4], (((-b_1)) / 2, ((-b_1)) / 2, b_1))
n = 1 (slider from 1 to 6, step 1)
b_2: ((2 * sqrt(3)) * (5 - (2 * sqrt(5)))^(0.25))
h_2: 45 / b_2
h_3: sqrt(s'_3^(2) - b_3^(2))
d, H, I, face18, face19, face20, face21, edge25, edge26, edge27, edge28, edge29, edge30 = Prism(Polygon[(-3, -5, 0), (-3, 5, 0), (-3, -5 + s_4, 4.8)], (3, -5, 0))
b, D, E, F, G, face6, face7, face8, face9, face10, face11, edge9, edge10, edge11, edge12, edge13, edge14, edge15, edge16, edge17, edge18 = Prism(Polygon[(((-b_2)) / 2, ((-b_2)) / 2), (b_2 / 2, ((-b_2)) / 2), 5], (((-b_2)) / 2, ((-b_2)) / 2, h_2))
c, face12, face14, face15, face16, face17, face13, edge19, edge20, edge21, edge22, edge23, edge24 = Pyramid(Polygon[((-b_3), 0), Rotate[((-b_3), 0), 60°, (0, 0)], 6], (0, 0, h_3))
s_5: ((sqrt(2) * 3439^(0.25))) / 3
b_5: (20 * s_5 / 18)
b'_5: 20 / b_5
e, J, K, L, M, face22, face24, face25, face26, face23, face27, edge31, edge32, edge33, edge34, edge35, edge36, edgeJK, edgeKL, edgeLM, edge37 = Prism(Polygon[(((-b_5)) / 2, (-b'_5)), (((-b_5)) / 2, 0), (0, 18 / b_5), (b_5 / 2, 0), (b_5 / 2, (-b'_5))], (((-b_5)) / 2, (-b'_5), s_5))
s_6: 22 / sqrt(2.5^(2) + 7^(2))
f, N, O, P, face28, face30, face31, face29, face32, edge38, edge39, edge40, edge41, edge42, edgeNO, edgeOP, edge43 = Prism(Polygon[(0, 2.5), (7, 0), (0, -2.5), (-7, 0)], (0, 2.5, s_6))
list1: {a, b, c, d, e, f}
list2: {(face1 * 6), (face11 * 2) + (face6 * 5), (face12 * 6) + 42, face18 + face19 + face20 + (face21 * 2), (face27 * 2) + (face22 * 2) + (face24 * 2) + face23, (face28 * 4) + (face32 * 2)}
text1: "Volume: " + (Volume[Element[list1, n]]) + "  u³
Surface Area: " + (Element[list2, n]) + "  u²"
Q = Intersect(xAxis, yAxis)
R = Point(xAxis)
T = (0.8359999999999982, 1.1719999999999993)
U = (5.069599999999999, 1.1719999999999993)
V: (-0.35381, 0.2)
W: (5.55168, 0.2)
E_1: (-0.67851, 1.15)
F_1: (5.55168, 1.15)
S = Point(xAxis)
Z = Midpoint(edge11)
A_1 = Point(edge12)
g = Segment(E, A_1)
B_1 = Midpoint(g)
C_1 = Intersect(edge6, edge2)
D_1 = Point(edge3)
h = Segment(C_1, D_1)
G_1 = Midpoint(h)
A_2: (0, 0, 0)
B_2: (0, 0, 4)
C_2: (4.5, 0, 2)
a_1: 2
D_2: (4.5, 4, 2)
E_2: (0, 4, 0)
F_2: (0, 4, 4)
G_2: (-4.5, 2, 4)
H_1: (-4.5, 2, 0)
poly1_1, c_1, a_2, b_4 = Polygon(A_2, B_2, C_2)
poly2_1, f_1, d_1, e_1 = Polygon(D_2, E_2, F_2)
poly3_1, h_1, a_3, e_2 = Polygon(A_2, E_2, H_1)
poly4_1, g_1, b_6, f_2 = Polygon(B_2, F_2, G_2)
poly5_1, b_7, c_2, d_2, f_3 = Polygon(B_2, C_2, D_2, F_2)
poly6_1, a_4, c_3, d_3, e_3 = Polygon(A_2, C_2, D_2, E_2)
poly7_1, a_5, b_8, g_2, h_4 = Polygon(A_2, B_2, G_2, H_1)
poly8_1, e_4, f_4, g_3, h_5 = Polygon(E_2, F_2, G_2, H_1)
i_1 = Segment(G_2, A_2)
I_1 = Midpoint(i_1)
j_1 = AngularBisector(F_2, B_2, G_2)
k_1 = AngularBisector(G_2, F_2, B_2)
J_1 = Intersect(k_1, j_1)
l_1 = AngularBisector(A_2, B_2, D_2)
m_1 = AngularBisector(D_2, A_2, B_2)
Pointface19 = PointIn(face19)
Pointface32 = PointIn(face32)
K_1 = Intersect(edge43, edge38)
i = Segment(K_1, O)
L_1 = Midpoint(i)
M_1 = Point(edge40)
j = Segment(P, M_1)
N_1 = Midpoint(j)
O_1 = Point(edge18)
k = Segment(O_1, E)
l = Segment(D, G)
P_1 = Intersect(l, k)
m = Segment(F, P_1)
p = Segment(E, G)
q = Segment(F, O_1)
r = Segment(D, F)
Q_1 = Intersect(r, p)
s = Segment(O_1, Q_1)
R_1 = Intersect(s, m)
t = Segment(R_1, D)
n_1, p_1 = AngularBisector(edge29, edge30)
q_1, r_1 = AngularBisector(edge29, edge28)
S_1 = Intersect(p_1, r_1)
T_1 = Point(edge26)
s_1 = Segment(I, T_1)
U_1 = Midpoint(s_1)
V_1 = Point(list1)
t_1 = Segment(H, V_1)
W_1 = Midpoint(t_1)
Z_1 = Point(edge25)
i_2 = Segment(Z_1, I)
H_2 = Midpoint(i_2)
I_2 = (-4.050080775387997, 0.01726553975091569, 0)
J_2 = Point(edge22)
j_2 = Segment(I_2, J_2)
K_2 = Midpoint(j_2)
k_2, l_2 = AngularBisector(edge22, edge23)
L_2 = Point(k_2)
M_2 = Intersect(l_2, k_2)
N_2 = Midpoint(L_2, M_2)
o = Distance(edge21, edge22)
m_2 = Segment(K_2, M_2)