A wire that is 16 centimeters long is shown below. The wire is cut into two pieces, and each piece is bent and formed into the shape of a square. Suppose that the side length (in centimeters) of one square is $x$, as shown below. (a) Find a function that gives the total area $A(x)$ enclosed by the two squares (in

Step 1 ：Given a wire that is 16 centimeters long, it is cut into two pieces, and each piece is bent and formed into the shape of a square.

Step 2 ：Suppose that the side length (in centimeters) of one square is \(x\).

Step 3 ：The total length of the wire is 16 centimeters. If one square has side length \(x\), then it has a perimeter of \(4x\). The remaining wire is then \(16 - 4x\), which forms the second square.

Step 4 ：The side length of the second square is therefore \((16 - 4x) / 4 = 4 - x\).

Step 5 ：The area of a square is given by the side length squared. So the total area \(A(x)\) enclosed by the two squares is \(x^2 + (4 - x)^2\).

Step 6 ：Simplify the equation to get the final function that gives the total area \(A(x)\) enclosed by the two squares.

Step 7 ：\(\boxed{A(x) = 2x^2 - 8x + 16}\)