UKMT Junior Mathematical Challenge, 2015

The diagram shows four shaded glass squares, with areas $1\text{ cm}^2$, $4\text{ cm}^2$, $9\text{ cm}^2$ and $16\text{ cm}^2$, placed in the corners of a rectangle. The largest square overlaps two others. The area of the region inside the rectangle but not covered by any square (shown unshaded) is $1.5\text{ cm}^2$. What is the area of the region where squares overlap (shown dark grey)?

(A) $2.5\text{ cm}^2$ (B) $3\text{ cm}^2$ (C) $3.5\text{ cm}^2$ (D) $4\text{ cm}^2$ (E) $4.5\text{ cm}^2$