 In order to find the shaded region, we'll need to find the area of the circle and subtract the area of the square. Area of a circle is found with pi times radius squared. Area of a square is just side length raised to the second power. So, we already know the radius of the circle, and that's 6. So that means this length is 6, and so are all of these other lengths, equal to 6. And so, to find one side length of the square, we can consider this triangle. We know it's an isosceles triangle because two of the legs are 6. This angle happens to be 90 degrees, and the reason it's 90 degrees is there are four of those central angles that make up a full circle, and 360 divided by 4 is 90. So we have a 30, 60, 90 triangle. We know the n-length is 6, and so that means the side length of the square is the hypotenuse. In other words, it's 6 root 2. So now we have the radius of the circle, which we know to be 6. So we have pi times 6 squared minus a side length of the square. Side length of the square was 6 root 2 raised to the second power, and 6 squared is 36, so we have 36 pi minus... Well, take care here. 6 root 2 squared is 6 times root 2 squared, which squares both 6 and root 2. And so we have 6 squared times square root of 2 squared. So we have 36 pi minus 6 squared, which is 36, and root 2 squared, and square root of 2 squared are opposites. So we have times 2. And so the exact area, because it asks us for the exact area of the shaded region, would be 36 pi minus 36 times 2, which is 72 square units. And there we go. What fun.