The figures below are made out of circles, semicircles, quarter circles, and a square. find the area and the perimeter of each figure and give your answers as a completely simplified exact value in terms of π (no approximations).

I.  ABCD is a square so  ∡BCD=90°
   |BC|²+|CD|² = |BD|²
   8² + 8² = |BD|²
     |BD|² = 8²·2
     |BD|  = √[8²·2]
     |BD|  = 8√2

II. Circular segment BCD is a quater of circle (because ∡BCD=90°)
R=8

So the lenght of arc BD:     

Perimeter of the figure:    
                                      

The area of circular segment BCD: 
                                             
III. The area of triangle BCD:
                                                
IV. The area of figure: