Can you wrap your brain around these puzzles?

This week, our puzzles involve measurement and area.  The diagrams are not to scale (on purpose), so you'll need to put on your thinking cap :)

PUZZLE 1:

A house has 4 rooms as shown in the floorplan diagram below.  The area of 3 of the rooms has already been calculated.  Can you determine the area of the final room  (shaded area)?

PUZZLE 2:

Look at the diagram below.  Can you find the missing dimension?

CLICK HERE TO SEE THE SOLUTIONS (scroll past the new puzzle)

SOLUTIONS FROM LAST WEEK:

PUZZLE 1:

PUZZLE 2:

This puzzle was rather difficult.  The first step was to determine the area of the newly formed shape.  Since we know that the original cross had an area equal to 5 "squares" (each square having a dimension of 1 toothpick x 1 toothpick), then we can calculate that the new shape must have a total area of 4 "squares" because it is 80% of the original.  The following solution is one possible way of solving this puzzle.  If we imagine this shape without the notch removed, then we have a triangle which represents half of a rectangle with dimension of 3 x 4.  The rectangle in this case would have an area of 12 "squares", so the triangle would have an area of 6 "squares".  Since 6 is 2 more than what we want (remember, we need a final area on only 4 "squares"), we can achieve this by moving 3 of the toothpicks inward to form a notch that reduces the area by 2 "squares".