Henry Ernest Dudeney/Modern Puzzles/133 - A Problem for Surveyors

Modern Puzzles by Henry Ernest Dudeney: $133$

A Problem for Surveyors

There are tricks in every trade, and the science of numbers contains an infinite number of them.

In nearly every vocation of life there are little wrinkles and short cuts that are most useful when known.

For example:

A man bought a little field, and here is a scale map that was given to me.

I asked my surveyor to tell me the area of the field,

but he said it was impossible without some further measurements;

the mere length of one side, $7$ rods, was insufficient.

What was his surprise when I showed him in about two minutes what was the area!

Can you tell how it is to be done?

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $133$. -- A Problem for Surveyors
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $263$. A Problem for Surveyors