Suppose you draw a square that has bright red sides and has area 16. Draw the midpoints of the four sides, and draw a square with those points as vertices. Let's say the sides of that square are yellow. Draw the midpoints of the yellow sides and draw a square with those points as vertices. Let those sides be green. What's the area of the green square?

## Solution

4 (each green side is 2). Extend the problem: What's the area of a triangle with red legs and yellow hypotenuse? (2). What's the area of a triangle with yellow legs and a green hypotenuse? (1) Check: do all the areas you found add up to 16? Also: What's the area of the yellow square? Also: if you keep drawing smaller and smaller squares in the same way, will you get to a square having area 1?