Carl is trying to find solutions to a geometric puzzle.  He has a square plot of land that he needs to reserve 1/4 for himself and divide the remaining 3/4 equally and in similar shape, among his 4 children.  There are two possible solutions.  Can you solve the puzzle?


Solution #1 - Squares

First, Carl divides his as to reserve to himself one-fourth in the form of a square.

Geometric Puzzle #1

Then, Carl takes the remaining 3/4 shape and scales it down by 1/4.  He then, multiplies the shape into 4 identically shaped pieces, and aranges them so that they fit into the original 3/4 shape.

Geometric Puzzle #1 Solution 1

Solution #2 - Rectangles

First, create a triangle that is 1/4 the size of the square.

Now, with straight lines, create two squares.

Proceed to disect the two squares with horizontal lines creating 4 triangles.

Then, disect one of the resultuing triangles from each square.  The shape of land for each of his four children is divided evenly and is the same shape.