Area between $ 2 y = 4 \sqrt{x}$, $y = 4$, and $2 y + 4 x = 8 $ Sketch the region enclosed by the curves given below. Then find the area of the region.
$ 2 y = 4 \sqrt{x}$, $y = 4$, and $2 y + 4 x = 8 $
Attempt at solution:
I guess I'm supposed to divide the areas into several parts, and then sum up the areas of those parts.
Wolfram alpha shows the sketched area... and I don't think those are the correct sketched areas, because the answer 14 isn't a correct answer.
So can someone tell me which sketched areas am I even looking at?

Here's the region:

You can perform the integration in two parts, where the limits are determined by the values of $x$ where the appropriate two equations have the same value.  I'll leave the details of that exercise to you but the result is ${11 \over 3}$.
Since you asked, here's the Mathematica code:
Plot[{4, 2 Sqrt[x], If[0 < x < 1, 4, Null], If[1 < x < 4, 4, Null], 
  4 - 2 x}, {x, -1, 5},
 PlotStyle -> {Red, Green, Red, Red, Orange},
 Filling -> {
   {3 -> {{5}, {None, Green}}}, 
   {4 -> {{2}, {None, Blue}}}
   }]

