Rectangles inside a square

Let the side lengths of rectangle $A$ be $a \times b$ as shown. Then we note that:

$\begin{cases} 2b+3a = 32 & ...(1) \\ 4b-2a & = 32 &...(2) \end{cases}$

From $2\times (1) - (2): \quad 8a = 32 \implies a = 4$ .

From $(2): \quad 4b-8=32 \implies b=10$ .

The area of the yellow region $A_{\color{#CEBB00}yellow} = \dfrac {32^2-6ab}2 = \dfrac {1024-240}2 = \boxed{392}$ .