Show square

Show the lines for dissection

Show the dissected objects

Show rotation 1

Show translation 1

Show rotation 2

Show translation 2

Show angles

Corresponding sides are:
AC = CD = DB = BA = Side of square
CF = DI = BH=AG = Let us call it Side 1
AF =CI = DH = BG = Let us call it Side 2

What can you say about the 4 triangles formed?

What can you say about FGHI?
FG  = AG - AF = Side 1 - Side 2
GH = BH - BG = Side 1 - Side 2?
So what figure is it?

Area of larger square = 
Area of 4  triangles plus square
= 2x(Side1xSide2) + (Side1-Side2)*(Side1-Side2)
=Side1² + Side²
= Sideofsquare²

csquare = 5 (slider from 4 to 20, step 1)
A = (-0.7, -0.74)
B = Point(Circle[A, csquare])
a = Segment(A, B)
b = OrthogonalLine(A, a)
c = OrthogonalLine(B, a)
d = Circle(A, csquare)
e = Circle(B, csquare)
C = Intersect(d, b, 2)
D = Intersect(e, c, 2)
f = Segment(C, D)
g = Segment(B, D)
h = Segment(C, A)
i = true
E = (-2.26, -1.66)
j = Line(E, A)
k = OrthogonalLine(C, j)
l = OrthogonalLine(B, j)
m = OrthogonalLine(D, l)
F = Intersect(j, k)
poly1, f_1, a_1, c_1 = Polygon(A, C, F)
G = Intersect(j, l)
poly2, b_1, a_2, g_1 = Polygon(A, G, B)
H = Intersect(l, m)
poly3, h_1, b_2, d_1 = Polygon(B, D, H)
I = Intersect(k, m)
poly4, c_2, i_1, d_2 = Polygon(I, D, C)
n = false
poly5, i_2, h_2, g_2, f_2 = Polygon(I, H, G, F)
o = true
A' = Rotate(A, 90°, F)
C' = Rotate(C, 90°, F)
F' = Rotate(F, 90°, F)
poly1', f', a', c' = Polygon(A', C', F')
u = Vector(F, G)
A'' = Translate(A', u)
C'' = Translate(C', u)
F'' = Translate(F', u)
poly1'', f'', a'', c'' = Polygon(A'', C'', F'')
q = false
r = false
v = Vector(G, H)
A'_1 = Rotate(A, 90°, G)
G' = Rotate(G, 90°, G)
B' = Rotate(B, 90°, G)
poly2', b', a'_1, g' = Polygon(A'_1, G', B')
s = false
J = Translate(A'_1, v)
G'' = Translate(G', v)
B'' = Translate(B', v)
poly2'', b'', j_1, g'' = Polygon(J, G'', B'')
t = false
distanceCD = Distance(C, D)
distanceBD = Distance(B, D)
distanceAB = Distance(A, B)
distanceAC = Distance(A, C)
α = Angle(A, C, F)
β = Angle(F, A, C)
γ = Angle(B, A, G)
δ = Angle(G, B, A)
ε = Angle(D, B, H)
ζ = Angle(H, D, B)
η = Angle(C, D, I)
θ = Angle(I, C, D)
p = false
e_1 = Distance(C, F)
perimeterpoly4 = Perimeter(poly4)
Pointpoly4_1 = PointIn(poly4)
k_1 = Perimeter(poly4)
Pointpoly4 = PointIn(poly4)
u_1 = Vector(C, D)
v_1 = Vector(C, A)
side:(4.3 * 4.3)
side1:(1.8 * 1.8)
side2:(2.5 * 2.5)
C'_2 = Translate(C, v_1)
m_1 = OrthogonalLine(F, b_1)