Let's call the shape that you get by removing four mutually,r tangent quartercircles with radius 3 from a square with side length 3 a squircle' of side 3. {See the leftmost shape in the diagram below.) 1. What are the area and perimeter of a squircle of side 3'? {I} A single squircle has four points where the quartercircles that were removed met. Consider the following process: At step rt = ID we have a single squircle for which 3 = 2. At step rt = 1, we attach four squircles for which 3 = % . 2 = % to the squircle in step I], attaching one [at one of its points} to each point of the larger squirclc. [See the middle shape in the diagram above.) The resulting shape has 3 . 4 = 12 points (where quartercircles met} to which nothing is yet attached. Let's call these the ne points of the shape. At step rt = 2, we attach a squircle for which 3 = % - % = (TUE -2 = g to each of the free points in the shape in step 1. {See the rightmost shape in the diagram above.) The resulting shape has 3 - 12 = 3 - [3 - 4) = 32 - 4 = 36 free points. At step rt = 3. we attach a squircle for which 3 = i- % = (as - 2 = 312 to each of these the free points in the shape in step 2. {Draw your own picture!) The resulting shape has 3 -3e= 34314) =33-4= me free points. REpeat for each integer n 3': 3 . . . 2. Find formulas for the values of s for the squircles added at step it and for the number of free points of the shape obtained in step rt. f2} 3. Find a formula for the total length of the perimeter of the shape obtained in step rt. [2! 4. Find a formula for the total area of the shape obtained in step it. [2} 5. What are the total length of the perimeter and the total area of the shape obtained alter innitely many steps of the process? 3'3}