In the figure below, $\triangle ZAX$ is equilateral and has perimeter $30$.

What is the exact area of the quadrilateral $FLAX$? Explain how you determined your answer.

[asy]
pair f=(0,sqrt(3)); pair l=(2,sqrt(3)); pair a=(2,0); pair x=(0,0);
pair z=(f+l)/2;
dot(f); dot(l); dot(a); dot(x); dot(z);
draw(x--f--l--a--x--z--a);
draw(rightanglemark(x, f,l,5));
draw(rightanglemark(f, l,a,5));
draw(rightanglemark(l, a,x,5));
draw(rightanglemark(a, x,f,5));
label("$F$",f, NW);
label("$Z$",z, N);
label("$L$",l, NE);
label("$A$",a, SE);
label("$X$",x, SW);
[/asy]