Final answer:
Calculating the total perimeter involves using the properties of squares and quarter circles inscribed within them, applying the relationship between the diameter and the side length of the square, and combining these elements to represent the perimeter in terms of π.
Step-by-step explanation:
To calculate the total length of both the outside and inside perimeters of a pattern comprising quarter circles and squares, we need to understand a few basic geometric properties. Firstly, if we have a square with side length a, the perimeter of the square would be 4a. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square, meaning a = 2r, where r is the radius of the circle. Knowing this, we can understand that the perimeter (circumference) of the circle will be 2πr. Since we are dealing with quarter circles, each perimeter segment along a quarter circle will be πr/2. Combining this with the straight segments of the squares will allow us to calculate the total perimeter in terms of π.