A circle with a radius of 2.5 cm moves along the table so that its center goes around the contour of a square with a side

A circle with a radius of 2.5 cm moves along the table so that its center goes around the contour of a square with a side of 4 cm. What is the area of the part of the table formed by the trace of the circle, with an accuracy of 1 cm2?

The points of the circle as close as possible to the center of the square will describe a square with a side:

4 – 2.5 = 1.5 cm.

And the most distant ones are a square with a side:

4 + 2.5 = 6.5 cm.

Then the area of the table part formed by the trace from the circle will be equal to the difference between the areas of these squares:

6.5 ^ 2 – 1.5 ^ 2 = (6.5 – 1.5) * (6.5 + 1.5) = 5 * 8 = 40 cm ^ 2.