Notes
tilted rectangles solution

Solution to the Tilted Rectangles Puzzle

Tilted Rectangles

The two rectangles are congruent. What’s the shaded area?

Solution by Area of a Parallelogram

Tilted rectangles labelled

With the points labelled as above, triangles GFEG F E and IBCI B C are congruent as are triangles FDEF D E and JIHJ I H. This means that the yellow rectangle, KJBAK J B A, and the parallelogram HGDCH G D C have the same area.

Thinking of HCH C as the base of this parallelogram, as this is the same as the height of the rectangle, the horizontal width of the parallelogram must be the same as that of the yellow rectangle. Since FEF E has the same length as BCB C, this means that the horizontal distance of EE from HCH C is the same as the length of ACA C. So ACA C has length 88.

Now thinking of GHG H as the base of the parallelogram, its “height” above this base is the length of GEG E, which is 88. Therefore the area of the parallelogram is 3×8=243 \times 8 = 24.

Since the parallelogram and yellow rectangles have the same area, the shaded region has area 2424.