Answer to Triangle Puzzle

Solution The slanting upper edge of the upper figure is not a straight line. It is made up of two lines that meet where they touch area C. This edge bends downward, so the area of the figure is 32. For the lower figure, the slanting upper edge is also made up of two lines that meet where they touch area C. This edge bends upward so the area of the figure is 33. The difference accounts for the hole.
The hypotenuses of triangles A and B have different slopes, therefore, both upper and lower 5x13 figures are quadrilaterals, not a triangles. The triangles A and B have areas of 12 and 5 and the other two pieces have areas of 7 and 8. The total area of the four pieces is 32 for each of two the figures. If the upper figure is rotated 180° and moved over the lower figure as shown below, the resulting rectangle has an area of 65. This is twice the area of 32 for the four pieces plus the area of the hole.