Hello, nkline!

If that's all that's given, we can't solve the problem.

$\displaystyle \text{I have a piece of fabric (shaded region) with measurements:}$

. . $\displaystyle a = 25,\;b = 18.384,\;c = 18.384\text{ inches.}$

$\displaystyle \text{It is bordered on three sides with a 6-inch wide strip of fabric.}$

$\displaystyle \text{What are the measurements of }\,x,\:y,\,\text{ and }\,z\:?$

I will assume that we have isosceles trapezoids: .$\displaystyle b = c,\;y = z$

But, even then, there is insufficient information.

Code:

x
D * - - - - - - - * C
/ \
/ * * \
/ 6 * a * 6 \
/ * - - - * \
y / /:::::::::\ \ y
/ /:::::::::::\ \
/ b/:::::::::::::\b \
/ * 6 /:::::::::::::::\ 6 * \
/@ * /:::::::::::::::::\ * \
A * - - - * - - - - - - - - - * - - - * B

We need another piece of information:

. . the base angle of the trapezoids $\displaystyle \,\theta$

. . or the length of the base of the inner trapezoid.