How much material do you need to fence a plot?

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

20 August 2017

After reading the article on the shapes of plots (Sunday Nation, July 30, 2017), Chegge Gitongah sent in a question about fencing. He wrote: “Now that you've enlightened us on measurement of a quarter an acre, talk about fencing – number of possible posts, number of strands of wire/metres and fastening pins to use.”

The number of fastening pins (“U” nails) is equal to the number poles multiplied by the number of strands of fencing wire from top to bottom.

The number of strands is equal to the height of the poles from ground level divided by the desired spacing between the strands.

The length of fencing wire is equal to the perimeter of the plot (that is, total distance all round) multiplied by the number of strands.

The number of poles is equal to the perimeter of the plot divided by the desired spacing between poles.

Finally; the perimeter of the plot depends only on the shape of the plot. It has no relationship whatsoever to the area!

Let me illustrate. Suppose you want to fence a 200ft-by-200ft square plot. The total distance around it is 800ft. If you put the poles 10ft apart, you would need 80 of them. What if the land was half that size; that is, 200ft-by-100ft?

The perimeter of the half-size plot is 600ft; therefore, you would need 60 fencing poles spaced at 10ft from each other.

The area has been divided by two but the perimeter reduces by only 25%.

The reason why there appears to be a discrepancy is that a square has higher symmetry than a rectangle. You can turn a square four times without any apparent change but a rectangle will only go twice.

Interestingly, if the shape is awkward enough, a smaller plot can have a longer perimeter than a larger one. Suppose you have three ‘50x100’ plots that are surveyed in such a way that they are touching on the 50ft sides. That is, the whole parcel measures 50ft by 300ft. The total distance all around is 700ft.

Now let’s compare this to another arrangement of four ‘50x100’ plots placed with the 100ft sides touching. They for a 200ft by 100ft parcel. The total perimeter is now 600ft. Even though the area is larger, the perimeter is smaller than that of the three ‘50x100s’.

In the case of rectangular plots, the ratio of length to width is a more important factor than the area.  In the three ‘50x100’ plots above, this ratio is 6:1 while in the case of four ‘50x100s’, it is 2:1.

The question that remains is this: what shape has the smallest perimeter for a given size of land? I will leave you to think about it.  Meanwhile; the important lesson to take away today is that, if you want to know how much materials are need to fence a plot, go out and measure the land!