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]

Aspacecraft can attain a stable orbit 300 kilometers above earth if it reaches a velocity of 7.7 kilometers per second. the formula for a rocket's maximum velocity v in kilometers per second is vequalsminus0.0098tplusc ln upper r, where t is the firing time in seconds, c is the velocity of the exhaust in kilometers per second, and r is the ratio of the mass of the rocket filled with fuel to the mass of the rocket without fuel. find the velocity of a spacecraft whose booster rocket has a mass ratio of 20, an exhaust velocity of 2.1 km/s, and a firing time of 15 s. can the spacecraft achieve a stable orbit 300 km above earth?