[Solved]How to Integrate from an implicit function?

Questions
1

I am having a hard time c calculating the Area from an implicit function.
I am trying to integrate an area under the function implicitly stated as next.
I have used this resource so I tried:

Open in Wolfram Cloud ↗

The problem is that the last result of N[%] is not accurate as far as I understand.

Is there anyway to get this to work using basic methods and without getting into double integration steps?

The area of that region in the picture is in fact: 1/6.

2

I am sorry.
I did everything wrong, including explaining the area.
I found the solution:

Open in Wolfram Cloud ↗
3

reg = ImplicitRegion[Sqrt + Sqrt[y] <= 1, {x, y}]; Area[reg]
(* 1/6 *)