Notes
three rectangles as a triangle solution

Three Rectangles as a Triangle

Three Rectangles as a Triangle

These three overlapping rectangles are congruent, each with area 44. The black dots mark the midpoints of the short sides. What total area is covered by this design?

Solution by Area of a Rectangle and Triangle

Three rectangles as a triangle labelled

With the points labelled as above, AA is the midpoint of the short side of a rectangle and CC is the midpoint of the long side. Therefore, triangle ABCA B C has area one eighth of the area of the yellow rectangle. The overlapping regions comprise six of these triangles, so have area 33. The total area is then 3×43=93 \times 4 - 3 = 9.