Tag Archives: area

Challenge: area of a parallelogram

Posted on June 24, 2021 by Brent

And now for something completely different!1 Suppose we have a parallelogram with one corner at the origin, and two adjacent corners at coordinates and . What is the area of the parallelogram? There are probably many different ways to derive … Continue reading →

Posted in challenges, geometry | Tagged , | 18 Comments

Area paradox unmasked

Posted on May 8, 2011 by Brent

In my last post I presented a paradox, where a set of four pieces forming an 8×8 square could apparently be rearranged to form a 5×13 rectangle, summoning an extra unit of area out of thin air. Quite a few … Continue reading →

Posted in geometry, pictures, puzzles, solutions | Tagged , , , | 1 Comment

An area paradox

Posted on May 2, 2011 by Brent

Here’s a fun paradox which has been around for quite a while and was apparently a favorite of Lewis Carroll. As you can verify for yourself, the two figures above are composed of two different rearrangements of the same four … Continue reading →

Posted in challenges, geometry, paradox, pictures | Tagged , , | 18 Comments