Three Squares in a Hexagon

Strategies and Hints

  1. 12 + 52 = 26   32 + 32 = 18   42 + 22 = 20

    For each square in the figure, it is possible to find a right triangle with integral sides so that the hypotenuse of the right triangle equals the side of the square.

  2. All vertices in the figure have integral coordinates.

  3. Three of the vertices of the hexagon are on the edges of a 12-inch square. The area of the hexagon can be found by subtracting from 144 as shown below.

Solution

The area of the hexagon can be found by subtracting the shaded area from the area of the 12-inch by 12-inch square.

Since 144 - 44 = 100, the area of the hexagon is 100 sq in.