RectTriArea Gray

Change the rectangle so that both shapes have the same estimated area.

20

median = 60

A = (-10, -1)
B = (-4, -1)
poly1, a, b, c, C = Polygon(A, B, 3)
perim: (3 * a)
areaT = Area(poly1)
D = (0, 0)
d = Circle(D, perim / 2)
E = Point(d)
e = Segment(D, E)
F = Point(e)
f_1 = OrthogonalLine(F, e)
g = OrthogonalLine(D, e)
h = Circle(F, E)
G = Intersect(h, f_1, 2)
i = OrthogonalLine(G, f_1)
H = Intersect(g, i)
poly2, d_1, f, g_1, f_2 = Polygon(D, F, G, H)
j: poly2 / poly1
k = Perimeter(poly2)
p = Circle(D, perim / 3)
I = Intersect(p, d_1, 1)
a_1 = Segment(D, I)
b_1 = Segment(I, F)
b_2 = Segment(F, G)
r(x) = x^(2) - (perim / 2 * x) + Area[poly1]
l = Segment(D, F)
m: f_2 / g_1
K = Intersect(r, xAxis, 2)
n = Distance(I, K)
o: n / a_1
s = Circle(F, a - l)
t = OrthogonalLine(F, xAxis)
L, M = Intersect(s, t)
e_1 = Segment(F, M)
H_2: (x(D), Min[c, y(H)])
c_2 = Segment(H_2, D)
q = If(poly2 > poly1, 1, 0)
c_1 = Segment(H_2, H)
h_1 = Segment(M, G)
k_1 = Circle(H, c - c_2)
J, N = Intersect(k_1, i)
i_1 = Segment(H, J)
j_1 = Segment(J, G)
u: (100 / 9 * x(F))
text2: "" + (LaTeX[u]) + ""
mp = Midpoint(D, F)
A1: 60
A2: 55
A3: 50
A4: 62
A5: 50
A6: 70
A7: 66
A8: 54
A9: 65
A10: 64
A11: 70
A12: 65
A13: 72
A14: 72
A15: 50
A16: 60
A17: 70
A18: 63
A19: 68
A20: 69
A21: 50
A22: 80
A23: 55
A24: 62
A25: 65
A26: 50
A27: 65
A28: 50
A29: 50
A30: 50
A31: 50
A32: 68
A33: 50
A34: 100
A35: 75
A36: 50
A37: 52
A38: 65
A39: 61
A40: 59
A41: 56
A42: 50
A43: 50
A44: 50
A45: 60
A46: 56
A47: 90
A48: 50
A49: 70
A50: 50
A51: 50
A52: 60
A53: 75
A54: 50
A55: 68
A56: 51
A57: 80
A58: 65
A59: 50
A60: 68
A61: 60
A62: 55
A63: 50
A64: 75
list1: {A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13, A14, A15, A16, A17, A18, A19, A20, A21, A22, A23, A24, A25, A26, A27, A28, A29, A30, A31, A32, A33, A34, A35, A36, A37, A38, A39, A40, A41, A42, A43, A44, A45, A46, A47, A48, A49, A50, A51, A52, A53, A54, A55, A56, A57, A58, A59, A60, A61, A62, A63, A64}
B1: 50
B2: 55
B3: 60
B4: 65
B5: 70
B6: 75
B7: 80
B8: 85
B9: 90
B10: 95
B11: 100
list2: {B1, B2, B3, B4, B5, B6, B7, B8, B9, B10, B11}
v = Histogram(list2, list1)
w: poly1 - poly2
list3: (9 * list1 / 100)
list4: (9 * list2 / 100) - 0.25
l_1 = Histogram(list4, list3, true, 1 / 5)
p_1(x) = (2 * x^(2)) + (2 * Area[poly1]) - (Perimeter[poly1] * x)
O, P = Root(p_1)
answer: x = x(P)
list5 = DotPlot(list1)
dots = DotPlot(list3, 0.25)
Q: (x(F), Area[poly2] / 4)
m_1 = BoxPlot(-1, 0.75, list3)
n_1 = Mean(list3)
o_1: (5.4 * 4)
q_1 = Median(list1)
r_1 = Mean(list1)