Rearrange the same four pieces, and a square-sized hole appears from nowhere
Cut a right triangle into four pieces along specific lines, then rearrange those exact same four pieces into a slightly different triangle shape. Measure the area both times using the grid squares underneath, and the second arrangement is missing exactly one unit square compared to the first. No piece was removed. Where did the square go?
Reveal the answer
Neither 'triangle' is actually a true triangle: both hypotenuses are very slightly bent, bowing inward in one arrangement and outward in the other, by an angle too small to see at normal scale. That sliver of extra or missing area, spread thinly along the whole hypotenuse, accounts for exactly one square unit. The illusion has circulated in recreational mathematics for decades and was widely popularized through Martin Gardner's writing.
— Wikipedia, Missing square puzzle — recreational mathematics reference