# Solution to the [[Three Congruent Rectangles VI]] Puzzle +-- {.image} [[ThreeCongruentRectanglesVI.jpg:pic]] > The three rectangles are congruent. What fraction of the design is shaded? =-- ## Solution by [[Area of a Triangle]] and [[Congruent Triangles]] +-- {.image} [[ThreeCongruentRectanglesVILabelled.png:pic]] =-- Consider the diagram labelled as above. Triangles $A H G$ and $A H F$ share the base $A H$, and as $F G$ is [[parallel]] to $A H$, the points $F$ and $G$ have the same [[perpendicular distance]] to $A H$, so triangles $A H G$ and $A H F$ have the same [[triangle area|area]]. Since the rectangles are [[congruent]], line segments $C F$ and $B H$ have the same length, so so do $C B$ and $F H$. Therefore $A F$ is [[parallel]] to $B D$. Since also $A H$ and $D C$ have the same length then triangles $D B E$ and $A F E$ are [[congruent]]. The white regions therefore have the same area as triangle $A B H$, which comprises one half of one of the rectangles and so one sixth of the design.