Calculating the area and perimeter of the curve

Questions
1

curve = x - 2 Sqrt + y^2 == 0

For this curve, how can we calculate its area and perimeter?

area = 2 Integrate[Sqrt[2 Sqrt[x] - x], {x, 0, 4}]

Is the area-finding method shown above correct? What other methods can be used to calculate the area? How can its perimeter be solved with code?

2

I would consider this other way:

func = x - 2 Sqrt[x] + y^2;
ContourPlot[func == 0, {x, 0, 5}, {y, -2, 2}]
RegionMeasure[ImplicitRegion[func == 0, {x, y}]]
RegionPlot[func <= 0, {x, 0, 5}, {y, -2, 2}]
Area[ImplicitRegion[func <= 0, {x, y}]]
3

Thank you very much! The problem has been solved.