j: y = sqrt(3) / 2
A = (0, 0)
C = (12, 0)
lattice = Sequence(Sequence[(i, j), i, 6, 40], j, 0, 20)
B = Point(lattice)
t1, c, a, b = Polygon(A, B, C)
perim = Perimeter(t1)
area = Area(t1)
E: (0, 0)
l: (perim / 2 + sqrt((perim / 2)^(2) - (4 * area))) / 2
w: area / l
P: (l, w)
F: (0, w)
G: (l, 0)
q1, e_1, g, d_1, f = Polygon(E, G, P, F)
i = Perimeter(q1)
H: (w, l)
D: (perim, area)
ratio: l / w
EquilateralPoint: (0.5, sqrt(3) / 2)
TwoThirdsPoint: (0.5, 2 / 3)
K: (l, ratio)