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Patterns in Prague

Prague is an ancient city in the Czeck Republic. In Prague some of the sidewalks are made from small square blocks, 5 cm by 5cm. The blocks are in different shapes to make patterns. This is one of the patterns they make. In this pattern some triangular blocks are made by cutting a square in half diagonally. EXPLORE
  1. Is the segment labeled "A" the same length as the segment labeled "B"? Rotate the blue dot to explore.
  2. Find the area of the purple region. Rotate the red dots to rearrange the tiles as necessary.
  3. How would you go about finding the perimeter of the purple region?