Area of a Rectangle
Author: Edward M. Knote
Date: 11/10/06

In this worksheet you will investigate the area of a rectangle.

Investigation:
1) Move the sliders Base and Height and describe what happens to the image.
 2) What relationship does the number of squares have with the area of the rectangle?
 3) Is there a way to find the number of square with out counting them?
 4) What conjecture can you make about the formula for area of a rectangle?

Szerokość

Długość

POLE \;  \;  PROSTOKĄTA

P = a \cdot a

wzór

P = a \cdot b

 POLE \;  \; KWADRATU

długość = 8 (slider from 1 to 10, step 1)
A = (-3.6, -1.5333333333333332)
B = Point(Circle[A, długość])
b = Segment(A, B)
szerokość = 9 (slider from 1 to 10, step 1)
C = Point(Circle[A, szerokość])
d = Segment(A, C)
e = Circle(A, C)
f = OrthogonalLine(A, b)
D = Intersect(e, f, 1)
g = OrthogonalLine(B, b)
h = OrthogonalLine(D, f)
E = Intersect(g, h)
P, a_1, d_1, e_1, b_1 = Polygon(A, D, E, B)
F = Midpoint(A, D)
G = Midpoint(A, B)
H = Point(Circle[A, 1])
i = Segment(A, H)
I = Point(Circle[A, 2])
j = Segment(A, I)
J = Point(Circle[A, 3])
k = Segment(A, J)
K = Point(Circle[A, 4])
l = Segment(A, K)
L = Point(Circle[A, 5])
m = Segment(A, L)
M = Point(Circle[A, 6])
n = Segment(A, M)
N = Point(Circle[A, 7])
p = Segment(A, N)
O = Point(Circle[A, 8])
q = Segment(A, O)
Q = Point(Circle[A, 9])
r = Segment(A, Q)
s = Circle(A, H)
t = Circle(A, I)
c_1 = Circle(A, J)
f_1 = Circle(A, K)
g_1 = Circle(A, L)
h_1 = Circle(A, M)
k_1 = Circle(A, N)
p_1 = Circle(A, O)
q_1 = Circle(A, Q)
R = Intersect(s, a_1, 1)
S = Intersect(t, a_1, 1)
T = Intersect(c_1, a_1, 1)
U = Intersect(f_1, a_1, 1)
V = Intersect(g_1, a_1, 1)
W = Intersect(h_1, a_1, 1)
Y = Intersect(k_1, a_1, 1)
Z = Intersect(p_1, a_1, 1)
A_1 = Intersect(q_1, a_1, 1)
B_1 = Intersect(q_1, b_1, 1)
C_1 = Intersect(p_1, b_1, 1)
D_1 = Intersect(k_1, b_1, 1)
E_1 = Intersect(h_1, b_1, 1)
F_1 = Intersect(g_1, b_1, 1)
G_1 = Intersect(f_1, b_1, 1)
H_1 = Intersect(c_1, b_1, 1)
I_1 = Intersect(t, b_1)
J_1 = Intersect(s, b_1, 1)
i_1 = OrthogonalLine(R, a_1)
j_1 = OrthogonalLine(S, a_1)
l_1 = OrthogonalLine(T, a_1)
m_1 = OrthogonalLine(U, a_1)
n_1 = OrthogonalLine(V, a_1)
r_1 = OrthogonalLine(W, a_1)
s_1 = OrthogonalLine(Y, a_1)
t_1 = OrthogonalLine(Z, a_1)
a_2 = OrthogonalLine(A_1, a_1)
b_2 = OrthogonalLine(J_1, b_1)
c_2 = OrthogonalLine(I_1, b_1)
d_2 = OrthogonalLine(H_1, b_1)
e_2 = OrthogonalLine(G_1, b_1)
f_2 = OrthogonalLine(F_1, b_1)
g_2 = OrthogonalLine(E_1, b_1)
h_2 = OrthogonalLine(D_1, b_1)
i_2 = OrthogonalLine(C_1, b_1)
j_2 = OrthogonalLine(B_1, b_1)
K_1 = Intersect(b_2, d_1)
L_1 = Intersect(c_2, d_1)
M_1 = Intersect(d_2, d_1)
N_1 = Intersect(e_2, d_1)
O_1 = Intersect(f_2, d_1)
P_1 = Intersect(g_2, d_1)
Q_1 = Intersect(h_2, d_1)
R_1 = Intersect(i_2, d_1)
S_1 = Intersect(j_2, d_1)
T_1 = Intersect(a_2, e_1)
U_1 = Intersect(t_1, e_1)
V_1 = Intersect(s_1, e_1)
W_1 = Intersect(r_1, e_1)
Y_1 = Intersect(n_1, e_1)
Z_1 = Intersect(m_1, e_1)
A_2 = Intersect(l_1, e_1)
B_2 = Intersect(j_1, e_1)
C_2 = Intersect(i_1, e_1)
k_2 = Segment(J_1, K_1)
l_2 = Segment(I_1, L_1)
m_2 = Segment(H_1, M_1)
n_2 = Segment(G_1, N_1)
p_2 = Segment(F_1, O_1)
q_2 = Segment(E_1, P_1)
r_2 = Segment(D_1, Q_1)
s_2 = Segment(C_1, R_1)
t_2 = Segment(B_1, S_1)
a_3 = Segment(R, C_2)
b_3 = Segment(B_2, S)
c_3 = Segment(T, A_2)
d_3 = Segment(Z_1, U)
e_3 = Segment(V, Y_1)
f_3 = Segment(W_1, W)
g_3 = Segment(Y, V_1)
h_3 = Segment(U_1, Z)
i_3 = Segment(A_1, T_1)
D_2, D_4 = Intersect(q_1, a_1)
E_2, E_4 = Intersect(p_1, a_1)
F_2, F_4 = Intersect(k_1, a_1)
G_2, G_4 = Intersect(h_1, a_1)
H_2, H_4 = Intersect(g_1, a_1)
I_2, I_4 = Intersect(f_1, a_1)
J_2, J_4 = Intersect(c_1, a_1)
K_2, K_3 = Intersect(t, a_1)
L_2, L_3 = Intersect(c_1, b_1)
M_2, M_3 = Intersect(f_1, b_1)
N_2, N_3 = Intersect(g_1, b_1)
O_2, O_3 = Intersect(h_1, b_1)
P_2, P_3 = Intersect(k_1, b_1)
Q_2, Q_3 = Intersect(q_1, b_1)
R_2, R_3 = Intersect(p_1, b_1)
a = OrthogonalLine(D_2, a_1)
c = OrthogonalLine(E_2, a_1)
j_3 = OrthogonalLine(F_2, a_1)
k_3 = OrthogonalLine(G_2, a_1)
l_3 = OrthogonalLine(H_2, a_1)
m_3 = OrthogonalLine(I_2, a_1)
n_3 = OrthogonalLine(J_2, a_1)
p_3 = OrthogonalLine(K_2, a_1)
q_3 = OrthogonalLine(L_2, b_1)
r_3 = OrthogonalLine(M_2, b_1)
s_3 = OrthogonalLine(N_2, b_1)
t_3 = OrthogonalLine(O_2, b_1)
a_4 = OrthogonalLine(P_2, b_1)
b_4 = OrthogonalLine(R_2, b_1)
c_4 = OrthogonalLine(Q_2, b_1)
U_2 = Intersect(q_3, d_1)
V_2 = Intersect(r_3, d_1)
W_2 = Intersect(s_3, d_1)
Y_2 = Intersect(t_3, d_1)
Z_2 = Intersect(a_4, d_1)
A_3 = Intersect(b_4, d_1)
B_3 = Intersect(c_4, d_1)
C_3 = Intersect(e_1, a)
D_3 = Intersect(e_1, c)
E_3 = Intersect(e_1, j_3)
F_3 = Intersect(e_1, k_3)
G_3 = Intersect(e_1, l_3)
H_3 = Intersect(e_1, m_3)
I_3 = Intersect(e_1, n_3)
J_3 = Intersect(p_3, e_1)
d_4 = Segment(U_2, L_2)
e_4 = Segment(M_2, V_2)
f_4 = Segment(W_2, N_2)
g_4 = Segment(O_2, Y_2)
h_4 = Segment(Z_2, P_2)
i_4 = Segment(R_2, A_3)
j_4 = Segment(B_3, Q_2)
k_4 = Segment(J_3, K_2)
l_4 = Segment(J_2, I_3)
m_4 = Segment(H_3, I_2)
n_4 = Segment(H_2, G_3)
p_4 = Segment(F_3, G_2)
q_4 = Segment(F_2, E_3)
r_4 = Segment(D_3, E_2)
s_4 = Segment(D_2, C_3)
o = true
T2: "a =" + (LaTeX[długość]) + ""
T5: "Pole=" + (LaTeX[długość]) + "\cdot" + (LaTeX[szerokość]) + "=" + (LaTeX[szerokość * długość]) + ""
T6: "a=" + (LaTeX[szerokość]) + ""
T1: "b=" + (LaTeX[szerokość]) + ""