One-seventh area triangle

[1] These six extra triangles partially cover ABC, and leave six overhanging extra triangles lying outside ABC.

Focusing on the parallelism of the full construction (offered by Martin Gardner through James Randi’s on-line magazine), the pair-wise congruences of overhanging and missing pieces of ABC is evident.

As seen in the graphical solution, six plus the original equals the whole triangle ABC.

[2] An early exhibit of this geometrical construction and area computation was given by Robert Potts in 1859 in his Euclidean geometry textbook.

[3] According to Cook and Wood (2004), this triangle puzzled Richard Feynman in a dinner conversation; they go on to give four different proofs.

The area of the pink triangle is one-seventh of the area of the large triangle ABC.
Graphical solution to the one-seventh area triangle problem.
Congruence of edge lengths allows rotation of the selected triangles to form three equal-area parallelograms, which bisect into six triangles of equal size to the original interior triangle.