Replies to This Discussion

Permalink Reply by Mac Davis on May 18, 2009 at 20:48

No, you can't calculate the area of a 4 sided figure from just the lengths of the 4 sides. You have to know something such as the length of a diagonal or the angle between two of the sides.

For example, assume the lot has 4 sides, each 100 feet long. If the angle between two of the sides is 90 degrees, it has 10,000 square feet. If the angle between 2 sides is 45 degrees, it only has 7,068 square feet. If it had 1 degree angle between two of the sides, it will have approximately 314 square feet.

Draw it out on paper if you don't believe me.

Are any of the sides at right angles or parallel to each other?

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Permalink Reply by Mac Davis on May 19, 2009 at 2:03

OK, maybe I'll buck up, drag out my ancient math skills and determine the possible range of values for the area. What is the
length of the side opposite the 146' long side?

I got essentially the same question asked of me about 30 years ago, tried to do the calculus to find max/min values and gave up because it got too ugly. That was before we had computers, though. I can do it with a spreadsheet, brute force, and massive ignorance these days.

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Permalink Reply by The_Baron on May 19, 2009 at 2:44

Do you have a plat?

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Permalink Reply by The_Baron on May 19, 2009 at 2:45

http://www.mathopenref.com/trapezoidarea.html

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Permalink Reply by The_Baron on May 19, 2009 at 4:25

Thats why I wanted to know if he has a plat. But the principle is the same, You can take any tract and plot it on graph paper to see how many squares of known size are inside the lot.

That being said, we are talking about such a small tract, that it dosn't really matter.

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Permalink Reply by The_Baron on May 19, 2009 at 4:26

Perhaps this would be better:

http://www.mathopenref.com/polygonirregulararea.html

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Permalink Reply by Mac Davis on May 19, 2009 at 10:35

We have 4 sides.

We need to know the order they're in. i.e. You can put these four edges together 6 ways. Telling me which side is front and which is back will do. Swapping left and right doesn't affect the area.

We then need

a) the angle between any two sides.
b) the fact that two edges are parallel. (actually this is the same as "a)" ) 8-)
c) The fact that any corner is a right angle. (also the same as "a)" ) 8-)
-or-
d) the length of a diagonal.

We'll need to know which sides or corners the above measurement are between.

We can then calculate the area.

I'll eventually get around to doing a spreadsheet of all the possible angles of one corner and figure out an accurate approximation of the possible range of areas, but I need to know which lengths are the front and back sides. (Or do the work for each of the 3 possible combinations, which probably exceeds my interest in the issue.)

I'm assuming that the lot is convex.

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Permalink Reply by RAY on May 20, 2009 at 3:19

The sides ....................127 & 121

the back.......................147

the front......................39

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Permalink Reply by BirdDawg, plain ole' idiot on May 20, 2009 at 4:02

If the lot is in a subdivision, or if you have a good metes and bounds legal description, there will be bearings on each line. If this is the case, and the survey is accurate (that the bearings came from) the acreage can be calculated exactly.

If bearings are given, then, as a surveyor, that is how I would calculate it. But as has been stated, the lot is so small, there woild probably be very small, if any, difference from what has been stated by others on here.

But if a surveyor did a unit survey or unit calculations on this unit, that is how it would be done.

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Permalink Reply by Mac Davis on May 21, 2009 at 7:22

The minimum mathematical acreage it can be is 0.198. That's for a triangle 146+166+121, which is one of the limiting cases for how you can arrange the angles on the 4 sided figure.

That assumes the lot is convex, which seems like a really good assumption.

The real answer is probably closer to the .25 acre number guestimated before, assuming a reasonable lot shape.

I'll calculate a maximum size as a mathematical exercise, but that will take some more typing entering formulas, and trial and error.

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Permalink Reply by Mac Davis on May 21, 2009 at 8:02

OK, I stumbled across Brahmagupta's formula, which gives the maximum possible size for a quadrilateral, given the length of the sides.

The maximum area for these 4 sides is 0.2382 acres.

So the mathematically possible range of acreage is 0.1980 through 0.2382, or just under 1/5 to just under 1/4 acre. Just under 1/4 is the most reasonable estimate for a reasonable shaped lot.

It turns out that the maximum area does not depend on the order of the 4 sides.

(corrected typo)

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Permalink Reply by Mac Davis on May 21, 2009 at 8:09

kb said

"the largest possible size with the posted lengths of 4 sides is 0.27025"

Hmmm.... how'd you get that number?

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