Henry Ernest Dudeney/Modern Puzzles/109 - Squaring a Star/Solution

Modern Puzzles by Henry Ernest Dudeney: $109$

This six-pointed star can be cut into as few as five pieces that will fit together to form a perfect square.

To perform the feat in $7$ pieces is quite easy,

but to do it in $5$ is more difficult.

The dotted lines are there to show the true shape of the star, which is made of $12$ equilateral triangles.

Find the side of the equal square by calculating the mean proportional between $AB$ and $BC$.

Make $BD$ equal to such.

Drop a perpendicular from $A$ to $BD$ at $E$, and $AE$ will equal $BD$.

The rest follows straightforwardly.

Dudeney attributes this result to Edward Brind Escott.

Martin Gardner erroneously references the dissections illustrated by Harry Lindgren as Figures $3.3$ and $3.4$ in his Geometric Dissections, but these appear to be of the regular hexagon to the square.