Shocking fact when  quarter of an acre is nowhere near that size

JOHN WAIMIRI SENT me a very simple and straightforward request – the kind that would make you wonder why he doesn’t do it for himself.  This was it: “Convert 0.08ha to acres”. John did not explain why he wants to know the answer, whether he is selling or buying a piece of land.

So I quickly sent him a link to the Google converter which changes quantities from one unit to another. But then I started thinking about the question and realised that it probably has more than meets the eye.

We are accustomed to dealing with land in acres even though surveyors work with hectares (ha).  A hectare is the area equivalent to a square plot measuring 100m on all sides. One hectare is approximately equal to 2.47 acres.

Not only are we accustomed to dealing in land using acres, but also subdividing smaller plots come in halves, quarters, and eighths of an acre. I suspect that this was what John was wondering about: is 0.08ha a half or a quarter or an eighth?

The Google converter says that 0.08ha is equivalent to 0.198acre. So the question is: what fraction of an acre is this. Well, a half is 0.5, a quarter is 0.25 and an eighth is 0.125. Therefore, we can see that 0.198 is somewhere between a quarter and an eighth.

The exact midpoint between a quarter and an eight is 0.1875, or, as a fraction, three-sixteenths.

We get that by simply adding 0.25 to 0.125 and dividing the result by two. You can visualise this by first noting that a sixteenth is a half of an eighth; thus a sixteenth is an eighth plus another half of an eighth. Now, one acre has 43,560 square feet, so an eighth should have exactly 5,445sq.ft. If this area was surveyed in the shape of a regular rectangle (that is, the length twice as long as the width), it would measure approximately 52ft-by-104ft.

In Kenya, however, what we call an eighth is supposed to be 50ft-by-100ft. But the shocking fact is that our surveyors actually measure it in metres: 15m-by-30m which is about 48ft-by-96ft. Thus our so-called eighth of an acre is actually 4,608 square feet instead of the exact figure of 5,445 square feet. That is, over 15% smaller!

Back to John’s question: I think he was more interested in the measurements of this plot of land; the width-by-length. In that case, we can easily surmise that the 0.08ha comes from 20m-by-40m. When we convert these measurements to feet, it comes to approximately 65ft-by-130feet. Now a regular rectangular quarter would be about 74ft-by-148ft.

So, it turns out that John’s plot is somewhere between a 50-by-100 and a 74-by-148. But I bet whoever is selling this land is calling it a quarter acre. Obviously, it is nowhere near that size.