Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: In the diagram, $PQ$ and $RS$ are diameters of a circle with radius 4.  If $PQ$ and $RS$ are perpendicular, what is the area of the shaded region?

[asy]
size(120);
import graph;
fill((-1,-1)--(-1,1)--(1,1)--(1,-1)--cycle,mediumgray);
fill(Arc((0,0),sqrt(2),45,135)--cycle,mediumgray);fill(Arc((0,0),sqrt(2),225,315)--cycle,mediumgray);
draw(Circle((0,0),sqrt(2)));
draw((-1,-1)--(1,1)--(1,-1)--(-1,1)--cycle);
label("$P$",(-1,1),NW); label("$R$",(1,1),NE); label("$S$",(-1,-1),SW); label("$Q$",(1,-1),SE);

[/asy]
user