Unable to relate the given sources/set up equation with the given info to solve quadrilateral problem

Question

$ABCD$ is a square with area 625, $CDEF$ is a rhombus with an area of 500, area of the shaded region is $55x$. Find $x$ wherein $x$ is a single digit non-zero number.

Answer 1

$AB = BC = CD = AD = \sqrt {625} = 25$

$CD\times \text{alt rhombus} = 500$ so $\text {alt rhombus} = 20$.

Let the point where $BC$ intersects $FE$ be $X$ and consider the side of the triangle $XCE$.

$XC = 20$ and $CE = CD = 25$.

Can you finish it from there?

$XE = \sqrt {CE^2 - XC^2} =\sqrt{25^2 - 20^2} = 15$

.

Area of $\triangle XCE = \frac 12 20*15 =150$

.

Area of the white area within the trapezoid $DFXC$ is $500 - 150=350$.

.

Area of the shaded area is $625 - 350 = 275$

.

$55x = 275$

.

$x = \frac {275}{55} = 5$

Answer 2

$x^2 = 625$

$xy = 500$

$y^2 + z^2 = x^2$