How to survey a quarter acre plot as a rectangle

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

15 March 2020

John Onyango wants to know the best way to subdivide a parcel of land into quarter acre plots. He writes: “in Kenya, we are used to land being sub-divided into one-eights of an acre or 50-by-100 feet. How can I get a quarter acre as a rectangle, that is, what should its measurements be?”

Now I have touched on this subject in a past article where I explained that, strictly speaking, 50-by-100 feet is not an eighth of an acre and that even the 50-by-100 plots are actually just 49-by-98 feet.

It can be very tempting to think that, if an eighth is 50-by-100, then a quarter must be 100-by-200. After all, if we double the dimensions, we should get double the size, shouldn’t we? That is very wrong!

When both sides of the plot are doubled, the size increases four times over. Thus, the 100-by-200 would actually yield four plots of 50-by-100. That is, it would be a “half-acre”, not a “quarter”.

Now it is generally assumed that a quarter is 100-by-100 feet – a square shape. To convert this into a rectangle, we must first work out its area. The answer is 10,000square-feet. Next, we ask: what other dimensions can give the same result of 10,000sq-ft?

There is an infinite number of combinations of length and width that can give 10,000sq-ft. For example, 50-by200 is one of them; so too is 80-by-125; and so on.

The first one is restrictive in the dimensions and orientation of the house that can be built on it. The second one a little better; however, we might prefer a plot whose length is double the width – like the 50-by-100.

To get the dimensions, we need to do some mathematical manipulation before punching numbers into a calculator. We know that the area (A) is equal to the length (L) multiplied by the width (W).

We desire that L = 2W. So, the area will be A = L x W = 2W x W.

Now the area of a 100-by100 is 10,000sq-ft; so, 2W x W = 10,000. This simplifies to: W x W = 5,000. Therefore, the width of the plot should be the square-root of 5,000.

Punching this into the calculator reveals that the width of the plot is W = 70.7 feet. Consequently, the length should be twice this figure; that is, 141.4 feet.

Now measurements in the imperial units are cumbersome: You need a calculator to convert decimals to inches! The reason is that one foot has 12 inches; thus, 0.7 foot is equal to about 8.5 inches and 0.4 foot is approximately 4.25 inches.

So, John’s “quarter” acre plot should measure 70ft 8.5in by 141ft 4.25in. Admittedly, those are rather awkward dimensions, so I would propose that he rounds the off to 70-by-140. This gives an area of 9,800sq-ft; and if he is unhappy with the smaller area, he may use 75ft by 150ft (=11,250sq-ft).