What is the area of the trapezoid shown? Express your answer in simplest exact form. [asy] unitsize(1.5cm); pair a=(0,0); pair b=(1,sqrt(3)); pair c=(3,sqrt(3)); pair d=(4,0); draw(a--b--c--d--a); label("2",(a+b)/2,NW); label("2",(b+c)/2,N); label("2",(c+d)/2,NE); label("~$60^\circ$",a,NE); label("$60^\circ$~",d,NW); [/asy]
