Area of black Square?
I will assume that the side of the square is trisected.
Area of black square?
Code:A x E x F x B * - - - * - - - * - - - * | * * * * * | | * .*. * | | * .*:::*. * J | 3x | *:::::::* | 3x | * *:::* * | | * * * | | *θ *θ * * | * - - - * - - - * - - - * D x G x H x C
Let the side of square be
Note the right triangle at the upper-right.
Code:x F * * * * * * * B * θ * * * * * * J
This is the side of the shaded square.
Area of shaded square: .
In right triangle
Substitute into : .
The area of square
The area of the shaded square is one-thirteenth that of the original square.
I agree with the first response. More information should have been given. Also bjhopper is correct in asserting that the inner quadrilateral is a non-square rhombus when the outer quadrilateral is square. The attachment shows what I think is a reasonable interpretation of the problem and a solution for the area of the inner square.