Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: The convex pentagon $ABCDE$ has $\angle A = \angle B = 120^\circ$, $EA = AB = BC = 2$ and $CD = DE = 4$.  What is the area of $ABCDE$?

[asy]

unitsize(1 cm);

pair A, B, C, D, E;

A = (0,0);

B = (1,0);

C = B + dir(60);

D = C + 2*dir(120);

E = dir(120);

draw(A--B--C--D--E--cycle);

label("$A$", A, SW);

label("$B$", B, SE);

label("$C$", C, dir(0));

label("$D$", D, N);

label("$E$", E, W);

[/asy]
user