I have a conveyance deed with a 'parcel clause' that defines a piece of land being transferred (from vendor to purchaser) as being
$47'$ (N to S) in length on the Western boundary,
$43'$ in length on the opposite side,
$80'$ on the top side,
and $82'$ on the bottom side.
The area being transferred is defined in the parcel clause as $405~ \text{sq. yds}$. exactly. The question is how should this be represented on a map. I would hope there is only one solution.
If you made the bottom side (the $82'$ length) join the $47'$ length at a right angle, the area of the quadrilateral could be imagined as a rectangle with two triangles tacked on:
i.e. $\text{Area} = 80 \times 43 + 43 \times 2 \times \frac 12 + 80 \times 4 \times \frac 12 \\= 3440 + 43 + 160 \\= 3643~ \text{sq ft} = 404 \frac 79 ~\text{sq. yds.}$
which is not $405 \text{sq. yds.}$ exactly, so maybe a better question is what angle should the bottom side meet the N to S side to get exactly an area of $405 \text{sq. yds.}$ , while keeping all the side lengths the same?.
Thanks for any help.
I have to submit a map of what shape the piece of land looks like. The solicitor who drew up the conveyance deed showed this quadrilateral as a rectangle, yes a rectangle with the side lengths all annotated as above! Don't trust a solicitor to do the job right! I assume the Land Registry would reject my title plan if I tried to present the land as a rectangle on a map, given the legal definition of its area and dimensions is what is written in the 'parcel clause'.
The problem with this 'solution' is the 80 and the 43 are not actual sides of the quadrilateral. In essence I have picked from the deed plan numbers I like, the 82 and the 47, to be boundary lengths, while using the 80 and the 43 to be bearings (or vector magnitudes, or whatever the maths jargon is) rather than sides of the quadrilateral. Sure, the area calculated from such an distasteful interpretation of the deed plan drawing is close to area of 405 sq. yds. but I'm sure accuracy is essential so I think my interpretation of the shape may not be right. For a consistent interpretation of the deed plan, y needs to be 80 and x to be 43.
My dodgy interpretation of parcel clause and deed plan that gives an area close to 405 sq. yds
One advantage of the above interpretation is that it joins well with land parcels to the west and to the south, and the curtilage (legal boundaries as opposed to physical boundaries?) on the north and east sides matches closely with topographical features that are defined on an Ordnance Survey map. Other deed plans I have seen quote the areas to fractions of so many "ninths", which makes me doubt whether rounding is acceptable in this business.
The parcel to the South is defined with a particular area and with the dimensions of another irregular quadrilateral, whose sides by the way, are to be "enlarged or diminished as necessary" (to be consistent with the size of the land before the northern parcel was divided off, I wonder?) and whose definition is "only for illustrative purposes".
A lawyer's way of leaving the maths to someone else, which was fine until the State insisted on guaranteeing everybody's land title by setting up a central land registry, and in doing so does not want to risk guaranteeing title to mathematically impossible combinations of land parcels in case it has to pay compensation.
At least before when clients never understood lawyer gobbledegook parcel clauses, there was never any risk of a client making a professional negligence claim - they wouldn't know what the error was to claim for! Time to get a chartered surveyor in and get title by making an adverse possession claim for the entire area defined by the surveyor (using the physical boundaries) and chuck the lawyer garbage parcel clauses, along with the title deeds, in the rubbish bin, methinks. Lawyers are not mathematicians, are they?