$Area \:of\: quadrilateral\:\: ABCD$
$ =Area\:of\:triangle\:ABF\:+Area\:of\:Triangle\:BCF$
$+Area\:of\:Triangle\:CDE\:+Area\:of \:Triangle\:ADE$

Please move the vertices A,B,C,D of the quadrilateral 
in order change the area of triagles.

Author- Tharanath
License- CC BY SA 4.0

Please drag the vertices of this quadrillateral
to change the area.

Area of a Rectangle

A = (-4.624977423960221, -6.738646121229521)
B = (-0.4645065934915156, 4.464907472246965)
C = (11.51170586850055, 4.464907472246964)
D = (13.710811878891153, -6.976387311542019)
a = Segment(A, B)
b = Segment(B, C)
c = Segment(A, D)
d = Segment(C, D)
e = Area(A, B, C, D)
text1: "" + e + ""
f = Segment(A, C)
g = OrthogonalLine(D, f)
E = Intersect(g, f)
h = Segment(E, D)
α = Angle(A, E, D)
i = OrthogonalLine(B, f)
F = Intersect(i, f)
j = Segment(B, F)
β = Angle(B, F, A)
poly1, b_1, a_1, f_1 = Polygon(A, F, B)
poly2, d_1, c_1, e_1 = Polygon(C, E, D)
poly3, c_2, b_2, f_2 = Polygon(B, F, C)
poly4, d_2, a_2, e_2 = Polygon(A, E, D)
T1: poly1 + poly2 + poly3 + poly4
text3: "$= " + (LaTeX[poly1]) + "\:cm^{2}+" + (LaTeX[poly3]) + "\:cm^{2}+" + (LaTeX[poly2]) + "\:cm^{2}+" + (LaTeX[poly4]) + "\:cm^{2} $
$= " + (LaTeX[T1]) + "\:cm^{2}$"
t2: (f * j)
t3: (f * h)
t4: t2 / 2
t5: t3 / 2
t6: t4 + t5
text4: "$ OR \:\:\: $
$\:Area\:of\:Triangle\:ABC+Area\:of\:Triangle \:ADC$
$=\frac{AC×BF}{2}+\frac{AC×DE}{2}$
$=\frac{" + (LaTeX[f]) + "×" + (LaTeX[j]) + "}{2}+\frac{" + (LaTeX[f]) + "×" + (LaTeX[h]) + "}{2}$
$=\frac{" + (LaTeX[t2]) + "}{2}+\frac{" + (LaTeX[t3]) + "}{2}$
$=" + (LaTeX[t4]) + "+" + (LaTeX[t5]) + "$
$=" + (LaTeX[t6]) + "\:cm^{2}$"
text6: "$ Area\:of\:the \: polygon ABCD\:=\: " + (LaTeX[e]) + " $"