+678 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]
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+101 
+118725 
+36 Oct 16, 2021
+678
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