Consider the diagram below
with measurements
indicated on it. The rectangle
of diagonal 5 cm fit perfectly
into the circle. Calculate the
area of the shaded part of
the diagram, correct to two
decimal places.

To find the area of the shaded part, we first need to calculate the area of the rectangle and the area of the circle into which it fits. Given that the rectangle has a diagonal of 5 cm, we can say that this diagonal is also the diameter of the circle.

First, we calculate the radius of the circle, which is half of the diameter:

Now, we find the area of the circle using the formula:

Next, we can determine the area of the rectangle. The sides and must satisfy the equation (from the Pythagorean Theorem). To get the specific area, we’ll assume that the rectangle is a square for simplicity (this won’t affect our final area subtraction because area will still relate based on their dimensions being proportional). We’ll say:

The area of the rectangle is:

Finally, the area of the shaded part, which is the area of the circle minus the area of the rectangle, will be:

Thus, the area of the shaded part of the diagram, correct to two decimal places, is approximately 7.13 cm².