formula to measure acre, when all 4 sides are different size

[Unregistered]

Re: formula to measure squire yards, when all 4 sides are different size

Hi,I hope someone can help me.I am trying to figure out how to measure a odd parcel of land all 4 sides are different dimensions.

Here are the dimensions.

side A-B 43", side A-C 43.2" , side B-D 32.6" , side C-D 43.5" .

I am trying to buy the property and there seems to be conflict with the size?

Please help
Thanks

[JohnS]

Re: formula to measure squire yards, when all 4 sides are different size

Hi,I hope someone can help me.I am trying to figure out how to measure a odd parcel of land all 4 sides are different dimensions.

Here are the dimensions.

side A-B 43", side A-C 43.2" , side B-D 32.6" , side C-D 43.5" .

I am trying to buy the property and there seems to be conflict with the size?

Please help
Thanks

Two problems:
First " is the symbol for inches. Do you mean ' which is the symbol for feet?
Second, area of a four-sided figure is not fixed by the four sides alone. We need a diagonal or the angles.

[sridhar]

Re: formula to measure acre, when all 4 sides are different size

102',63.5'',53',71.3''

[duh]

I realize this thread is insanely old. It came up in a search that I did and realized how much bad info was posted.
One does not need to know angles in order to calculate the area of a scalene trapezoid, let alone any quadrilateral.
If all dimensions are known we can calculate the area.
I'm not writing a formula for this however, I will give a short description of how it is done for those that stumble upon this in the future.

Space of 100 x 97 x 50 x 49 =
First, start with a square 97 x 49= 4753 (a) Use the smallest sides in this example.
Make two squares out of the remainder from making the first square and find there areas, then divide by two
In this case 3 x 50 (b) and 1 x 100 (c). b = 150/2=75, c = 100/2=50.
Add a b c together = 4753 sq whatever dimension which = the area.
Figure out how to convert that to acres on your own.... it's easy!

[duh]

I actually forgot one of the remainders from the original square which would have been 1 x 97... 48.5 (d) total should have been 4801.5. It's not easy holding those numbers in your head for a while. You have the idea though.

[JohnS]

I realize this thread is insanely old. It came up in a search that I did and realized how much bad info was posted.
One does not need to know angles in order to calculate the area of a scalene trapezoid, let alone any quadrilateral.
If all dimensions are known we can calculate the area.
I'm not writing a formula for this however, I will give a short description of how it is done for those that stumble upon this in the future.

Space of 100 x 97 x 50 x 49 =
First, start with a square 97 x 49= 4753 (a) Use the smallest sides in this example.
Make two squares out of the remainder from making the first square and find there areas, then divide by two
In this case 3 x 50 (b) and 1 x 100 (c). b = 150/2=75, c = 100/2=50.
Add a b c together = 4753 sq whatever dimension which = the area.
Figure out how to convert that to acres on your own.... it's easy!

This is incorrect as the four sides alone do not define a unique shape. The four sides form a four-bar linkage which can flex into several shapes, but have limits where two sides flex into a single straight line. Consider a rectangle, four 90° corners and a pair of equal sides opposite each other, length, and width. The area is, of course, length x width.

But the same set of four sides can flex at the corners into a parallelogram, where the area becomes length x width x sin(theta), where theta is any of the four corner angles. Area of this four bar structure can vary from zero to the maximum of length x width. Since the same four-bar structure can have multiple shapes and areas, additional info is required to pin down the shape and area. This can be either diagonal or any of the four corner angles, but the area is indeterminate without more info.

For four unequal sides, the math is more complex, but the same basic result occurs. You need either an angle or diagonal to "fix" the structure into a rigid structure with determinate area. If the figure is flexed to form a cyclic quadrilateral, the area is given by Brahmagupta's formula, and this area is the maximum possible area for the given four sides. The area of the same four sides, flexed into other shapes is given by Breitschneider's formula if two opposing angles are known and is equal to or less than the area given by Brahmagupta's formula. The maximum area for your four sides is 4873.45, but it CAN be less depending on the shape it is flexed into.

[Chandra Sekhar]

Please help in calculating total acres

E-118.701
W-141.78
N-629.114
S-538.77

Thanks,
Chandra

[gubment_cheez]

You have not provided enough information to calculate the acres from your figures.
Brahmagupta's formula calculates your area as 71318.07 square units.
However I don't know if your units are in feet, meters, or inches, and cannot complete the conversion to Acres without this information.

[JohnS]

I agree with Gubment_Cheez that we need more information, both angular information (or bearings of the sides) and units. A quadrilateral is not fixed by the four sides alone as it can flex at the vertices. We need a diagonal or corner angles. Brahmagupta's formula is only valid for a cyclic quadrilateral (one that can be inscribed in a circle, or two opposite angle add to 180°). It is an upper bound for a general quadrilateral. There is another term that has to be subtracted (Bretschneider's formul;a) for a general quadrilateral; it depends on the sum of opposite angles.