The picture
Sam Loyd's Geometric Puzzle
From: Interactive Mathematics Miscellany and Puzzles
Source:
Solution: http://www.cut-the-knot.org/pythagoras/Loyds.shtml#sol
From Mathematical Puzzles of Sam Loyd selected and edited by Martin Gardner (Dover, 1959), came puzzle #36. The puzzle is framed into a story of an auction at which a plot of land comprising three squares surrounding a triangular lake was offered for sale. Sam Loyd states the puzzle thus:
The question I ask our puzzlists is to determine how many acres there would be in that triangular lake, surrounded as shown by square plots of 370, 116 and 74 acres. The problem is of peculiar interest to those of a mathematical turn, in that it gives a positive and definite answer to a proposition which, according to usual methods, produces one of those ever-decreasing, but never-ending decimal fractions.
From: http://www.cut-the-knot.org/pythagoras/Plato.shtml
Born in 1841, he invented (according to his own account) his first puzzle at the age of 9. When he was 16 he became problem editor of the Chess Monthly and made a good living of puzzle invention till his death in 1911. One of his problems (Fifteen) caused a national craze on both sides of the Atlantic. Some other puzzles also sold by the millions. Loyd's ingenuity might only be compared to that of his contemporary, H.E. Dudeney - England's greatest puzzlist.