DanielAttard
asked on
Need help calculating area of land with 4 unequal sides
How would I calculate the area of a parcel of land that has four unequal sides?
The four sides are:
104.641 feet X 33.528 feet X 18.655 feet X 110.683 feet
Thanks.
The four sides are:
104.641 feet X 33.528 feet X 18.655 feet X 110.683 feet
Thanks.
If you know the angle of any one corner, you can solve the problem.
Let ABCD be the corner points on your plot
AB = 104.641 feet
BC = 33.528 feet
CD = 18.655 feet
DA = 110.683 feet
========================== ========== ========== ===
Assume the angle ABC = 75 degrees
Now you can use the Law of Cosines to find the diagonal between B and C
http://mathworld.wolfram.com/LawofCosines.html
AC = sqrt( AB² + BC² - 2AB*cos(75)) = 101.281 feet
========================== ========== ========== ====
Now you have broken you plot into two triangles.
AB = 104.641 feet
BC = 33.528 feet
AC = 101.281 feet
and
AC = 101.281 feet
CD = 18.655 feet
DA = 110.683 feet
You can user Heron's formula to find the area of each triangle, and add them up to get the total area of your plot.
http://mathworld.wolfram.com/Semiperimeter.html
Let ABCD be the corner points on your plot
AB = 104.641 feet
BC = 33.528 feet
CD = 18.655 feet
DA = 110.683 feet
==========================
Assume the angle ABC = 75 degrees
Now you can use the Law of Cosines to find the diagonal between B and C
http://mathworld.wolfram.com/LawofCosines.html
AC = sqrt( AB² + BC² - 2AB*cos(75)) = 101.281 feet
==========================
Now you have broken you plot into two triangles.
AB = 104.641 feet
BC = 33.528 feet
AC = 101.281 feet
and
AC = 101.281 feet
CD = 18.655 feet
DA = 110.683 feet
You can user Heron's formula to find the area of each triangle, and add them up to get the total area of your plot.
http://mathworld.wolfram.com/Semiperimeter.html
I wonder if one angle is enough for this correct me if I am wrong here
Lets say we have 4 sides AB, BC, CD and DA
and lets say we know the angle B
so we can draw AB and BC with the angle between them as given
now to obtain side D , we take a compass and draw and arc of length CD with C as centre and a arc of length AD with A as centre ,
now these two arcs can cross each other at two places , producing two quadrilaterals , one convex and the other concave
*A
*B *D' * D"
*C
I hope the above diagram comes to scale (somewhat atleast ).. if it does ....you can see if we have angle B fixed , and all the 4 sides fixed , we still have two poinst satisfying for D , D' and D" ..such that AD' = AD" = AD and CD'=CD"=CD
Abhijit
Lets say we have 4 sides AB, BC, CD and DA
and lets say we know the angle B
so we can draw AB and BC with the angle between them as given
now to obtain side D , we take a compass and draw and arc of length CD with C as centre and a arc of length AD with A as centre ,
now these two arcs can cross each other at two places , producing two quadrilaterals , one convex and the other concave
*A
*B *D' * D"
*C
I hope the above diagram comes to scale (somewhat atleast ).. if it does ....you can see if we have angle B fixed , and all the 4 sides fixed , we still have two poinst satisfying for D , D' and D" ..such that AD' = AD" = AD and CD'=CD"=CD
Abhijit
Well, one angle (or one diagonal) is not strictly enough as avizit claims, as a diagonal/angle will determine both of the 2 triangles the shape is formed of, but not the layout: the second triangle could be in two positions: Adding more area to the first triangle (like in a usual rectangle), or subtracting it (like in a arrow-like V).
Foir instance, lenghts of 10m each of the four sides, and an angle of 90 degree, can form both a rectangle or a L shape with no area inside.
It is just a thought, in "real world" ones knows how the shape is, so no more meassuraments are necesaries except one diagonal (or angle).
BTW, meassuring an angle is very difficult in real world, while measuring a diagonal is easy, and calculating area from a diagonal is far more easy that from the angle, so better go for a diagonal.
Foir instance, lenghts of 10m each of the four sides, and an angle of 90 degree, can form both a rectangle or a L shape with no area inside.
It is just a thought, in "real world" ones knows how the shape is, so no more meassuraments are necesaries except one diagonal (or angle).
BTW, meassuring an angle is very difficult in real world, while measuring a diagonal is easy, and calculating area from a diagonal is far more easy that from the angle, so better go for a diagonal.
>> avizit
>> Sergio_Hdez
I agree with everything you've said. I was assuming a real world problem,
i.e. a convex polygon, from a surveyed plot plot plan.
If you wind up with a convex polygon, you can sill calculate the area by subtracting
the area of the smaller triangle from the area of the larger.
You have real trouble if you wind up with a degenerate bowtie quadrilateral.
*A
*B
*C
*D' * D"
>> Sergio_Hdez
I agree with everything you've said. I was assuming a real world problem,
i.e. a convex polygon, from a surveyed plot plot plan.
If you wind up with a convex polygon, you can sill calculate the area by subtracting
the area of the smaller triangle from the area of the larger.
You have real trouble if you wind up with a degenerate bowtie quadrilateral.
*A
*B
*C
*D' * D"
ASKER
Thank you for all your comments. I guess I should have provided a bit more information. I only know the angle of one of the corners, which is a right angle. Here is a sketch, showing the dimensions of each side:
110.683
A-----------------------
| ---------------
| -------------B
| /
| /
33.528 | / 18.655
| /
| /
C| __________________________ _______/ D
(right angle) 104.641
The AB side is a straight line, I just had a difficult time drawing it. I hope you get the idea of the layout. Can we calculate the area of this since we know the angle of C is 90 degrees?
110.683
A-----------------------
| ---------------
| -------------B
| /
| /
33.528 | / 18.655
| /
| /
C| __________________________
(right angle) 104.641
The AB side is a straight line, I just had a difficult time drawing it. I hope you get the idea of the layout. Can we calculate the area of this since we know the angle of C is 90 degrees?
By the method in my second post
I get a diagonal AD = 109.8811
And an area of 2778.225 sq ft
I get a diagonal AD = 109.8811
And an area of 2778.225 sq ft
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ASKER
That's great! Very understandable. I really appreciate your help with this. Thank you so much!
Do you know any of the angles?
Or one of the diagnol (corner to corner) measurements.
A four sided figure is not adequately defined by the lengths of its sides.