-1. Draw a regular hexagon then draw the six "alternate" vertices. (Skip one vertex - 1 to 3, 2 to 4 etc). If the area of the original hexagon is 6, what is the area of the internal hexagon that is formed?
-2. Inscribe a square in a circle of radius R. Draw an arc from one corner of the square with radius equal to the side of the square. The area formed between this arc and the circle is a crescent. Find the area of this crescent in terms of R.
-3. In the equations below, replace each letter with a number from 1 to 9, using each number only once:
a/b + c/12 = 1 1/12
d/e + 5/f = 7/8
g/h + 3/i = 1 1/2
Sometimes I get the feeling the whole world is against me, but deep down I know that's not true. Some smaller countries are neutral.