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

by : $133$

 * A Problem for Surveyors

Solution
The construction given below takes advantage of the fact that $\angle AFG$ is a right angle.


 * Dudeney-Modern-Puzzles-133-solution.png

Produce $GA$.

Construct $AC$.

Construct a straight line through $B$ parallel to $AC$ to meet $GA$ at $1$.

Construct $1D$.

Construct a straight line through $C$ parallel to $1D$ to meet $GA$ at $2$.

Construct $2E$.

Construct a straight line through $D$ parallel to $2E$ to meet $GA$ at $3$.

Construct $3F$.

Construct a straight line through $E$ parallel to $3F$ to meet $GA$ at $4$.

Construct $4G$.

Then $\triangle G4F$ is equal in area to the field $ABCDEFG$.