\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The door is composed of a rectangle with height 10 meters and width \( x \) meters, topped with a semi-circle of diameter \( x \) meters.
Find the area \( A \) of the door in terms of \( x \).
\( A = \)
\(\text{m}^2\).