Create diagrams for examples -see the patterns.

c = 6107

d = 78

e = 23

f = 134

(d+n)^2 {

d^2 = 6084 //first square in structure

f is divided into two pieces, 67+67

e is divided into two even pieces with one left over, 11+11+1^2

d^2 + e + f = 6141 //next square in structure

(n^2 - 1) + last piece of e = n^2 //next square in structure

d^2 + e + f + (n^2 - 1) + 2d(n-1) = (d+n)^2 //the large square

}

(x+n)^2 {

f is divided into two even pieces with two pieces, one and one left over

(n^2 - 1) + one of the leftover pieces of f = n^2 //first square in structure

(n^2 - 1) + f + 2d(n-1) = (x+n)^2 //the smaller square

}