No shape has the greatest area. You can make a circle the size of a fingernail, and a square the size of a house; you can make a trapezoid the size of a crumb, and a rectangle the size of a car. Since you can change the size of the shape, there is no true answer.
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A square will. The only shape that can enclose more area with the same perimeter is a circle.
In other words ... least fence for greatest area ... First place . . . Circle Second place . . . Square
You would find the area of the inside and outside shape (pretending that the inside shape was not in the outside shape). then, you would take the area of the outside shape and subtract the area of the inside shape.
In the phrase 'area of a shape', both area and shape are nouns. In your mind, add 'the', it helps to show that they are nouns: 'the area of the shape'.
Because area is a function of perimeter.