Square And Rectangle

The area of the square shown below is 8 x 8 = 64. The square is cut in the four parts A, B, C, and D, which are rearranged into the rectangle shown below. This rectangle has an area of 13 x 5 = 65.

The Question: How can you explain the difference in area?


Answer: The picture of the rectangle is deceptive! The line XY shown in the picture of the rectangle (see below) is not a line at all. The parts XU and VY have a gradient of 2 / 5 = 0.4, and the parts XV and UY have a gradient of 3 / 8 = 0.375. So, in fact, XUYV is a parallellogram with an area of 1, not a line!