The following diagram shows an 8x8 square decomposed and rea

The following diagram shows an 8x8 square decomposed and reassembled to form a rectangle. Examine the two figures. What is the problem? Explain what is happening.

The following diagram shows an 8 x 8 square decomposed and reassembled to form a rectangle. Examine the two figures. What is the problem? Explain what is happening. 5

Solution

In 8x8 square has an area of 64. We can cut the square into four pieces and reassemble to get a 5x13 rectangle with an area of 65. This means that there is an area increase of 1 despite assembling it from same area of square.

This is so because i f you check out the 5 x 13 rectangle, you will find that the pieces do not exactly cover the rectangle. There is a very narrow

parallelogram with two opposite corners at opposite corners of that

rectangle whose area is 1 square unit. That is because the slopes

of the diagonal edges of the two kinds of pieces are not exactly the

same, although they are close.