Difference in the area of total and half right trapezoid

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Srinivas

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Hi,

Could anybody explain me why the difference is coming.

Area of right trapezoid for the total figur I.e AEFD Value is 131978,
For ABCD Value is 62196
And for BEFC Value is 57630.

The sum of ABCD and BEFC should be equal to AEFD. Correct me if am wrong.
 

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Are you sure that D,C and F lie on a straight line? Same question for A,B,E.
 
Srinivas said:
Hi,

Could anybody explain me why the difference is coming.

Area of right trapezoid for the total figur I.e AEFD Value is 131978,
For ABCD Value is 62196
And for BEFC Value is 57630.

The sum of ABCD and BEFC should be equal to AEFD. Correct me if am wrong.
Click to expand...
Please post the EXACT and COMPLETE problem
Srinivas said:
The sum of ABCD and BEFC should be equal to AEFD
Click to expand...
The assumption above seem to be correct, if it is given that ABE and DCF are straight lines.

Is it given to you that the angle DAB = Angle FEA = 90o ? Does not look like that from your sketch.
 
Srinivas said:
Hi,

Could anybody explain me why the difference is coming.

Area of right trapezoid for the total figur I.e AEFD Value is 131978,
For ABCD Value is 62196
And for BEFC Value is 57630.

The sum of ABCD and BEFC should be equal to AEFD. Correct me if am wrong.
Click to expand...
Either I'm totally off this morning (always possible) or this figure violates the Pythagorean Theorem. I don't think the numbers in the diagram can be correct.

-Dan
 
Srinivas said:
Hi,

Could anybody explain me why the difference is coming.

Area of right trapezoid for the total figur I.e AEFD Value is 131978,
For ABCD Value is 62196
And for BEFC Value is 57630.

The sum of ABCD and BEFC should be equal to AEFD. Correct me if am wrong.
Click to expand...
Presumably you mean this:

1661000241677.png

But if we draw that, we get a different length for CF:

1661000306967.png

The whole figure is not a trapezoid, because, as others have pointed out, D, C, F are not collinear. So trapezoid AEFD is larger than the sum of the parts:

1661000497104.png
 
Thanks Dr.Peterson. even I am not sure whether it is Right Trapezoid or not, I have taken it from the land document.
Could you please tell me which tool or app did you use to draw the the diagram in your answer.
 
Srinivas said:
Thanks Dr.Peterson. even I am not sure whether it is Right Trapezoid or not, I have taken it from the land document.
Could you please tell me which tool or app did you use to draw the the diagram in your answer.
Click to expand...
I used GeoGebra (geometry mode), and typed in the coordinates of the points.

A land document should contain more information than those side lengths (primarily the directions of the sides); if you can show the actual document or the data it contains, there is probably more I can do, as I've worked with such things before.
 
Dr.Peterson said:
I used GeoGebra (geometry mode), and typed in the coordinates of the points.

A land document should contain more information than those side lengths (primarily the directions of the sides); if you can show the actual document or the data it contains, there is probably more I can do, as I've worked with such things before.
Click to expand...
Thanks Dr. Peterson. I have tried GeoGebra and totalled the interior angles but they are not even 360°. I assumed it as a quadrilateral because angles have not been given in the document. Could you explain me how to calculate the area of this one.
 
With a little change in the measurements the angles are coming to 360°. If they are not quadrilaterals how to measure the area of them.
 
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Srinivas said:
Thanks Dr. Peterson. I have tried GeoGebra and totalled the interior angles but they are not even 360°. I assumed it as a quadrilateral because angles have not been given in the document. Could you explain me how to calculate the area of this one.
Click to expand...
The sum of the interior angles of any quadrilateral is 360°. And any figure with four straight sides is by definition a quadrilateral. (But ABEFCD is a hexagon.) So, what is it that you added up? Please at least show us your figure, so we can tell what you are talking about!
Srinivas said:
With a little change in the measurements the angles are coming to 360°. If they are not quadrilaterals how to measure the area of this.
Click to expand...
As I said, to calculate the area, you need more information than you provided. Please either show the entire description of the property, or at least tell us one additional fact other than the sides.

As I said, a land document is required to give more information than just side lengths. Typically it will show the directions of the sides; if it didn't do that, it might possibly show the lengths of diagonals, which can be sufficient. But we can't help without seeing the details you are omitting.

But if you can draw it accurately, without guessing angles, then GeoGebra will calculate the area for you. So the hard part is not how to calculate the area, but how to specify the figure.
 
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Hi Dr. Peterson,

I have attached the drawn document. I have checked the areas separately two parts but they are not matching to the area of whole figure. The value of AC is 857. I do not know the value of AB and BC separately. Could you please do me the favour in calculating the area of ACDF, ABEF, BCDE and ACGH.

Regards,
Sri.
 

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Srinivas said:
Hi Dr. Peterson,

I have attached the drawn document. I have checked the areas separately two parts but they are not matching to the area of whole figure. The value of AC is 857. I do not know the value of AB and BC separately. Could you please do me the favour in calculating the area of ACDF, ABEF, BCDE and ACGH.

Regards,
Sri.
Click to expand...
Thanks. That helps a lot. The diagonal measurement determines the angles, and I can use the data shown to construct the figure in GeoGebra. Except ...

1661270764436.png1661270947632.png​

The last thing to construct was the 161-unit segment from E to B. It turns out that that distance has to be longer than that; you can see that a circle with that radius doesn't reach. (Even if it had, there would have been a problem, because I'd get two possible points. So this is not the best way to survey the land!)

Also, the 880 isn't quite accurate; and if it were not really a straight line, the sum would be even greater. So the data just aren't consistent in the first place, and I can't yet calculate the areas involving B.
 
Hi Peterson,

The point E is not given in the document, roughly I have mentioned it. The segment 161 units can be moved to fit vertically between AC and DF.
 
Srinivas said:
Hi Peterson,

The point E is not given in the document, roughly I have mentioned it. The segment 161 units can be moved to fit vertically between AC and DF.
Click to expand...
Do you mean that the number 310 is not really there, as you've implied the 292 in your original drawing also is not? Then what IS known? Do we know that DF is really a straight line?

Please show exactly what is really known. If you want a correct answer, we need the correct input.
 
In document it is showing straight and 310 is also there in surveyor's computer. 292 is not there.
 
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I got your point. Thanks a lot Dr.peterson. The distance of the EB segment has to be longer. Thanks a lot for your time and help. I really appreciate it.
 
Hi Dr. Peterson,
I have attached one more image . I am not able to understand what is 692 units between E and D because FE is 310 and the sum is more than FD 881units. As you have worked on these things before please reply if you have time. CD is 43 units not 48.
 

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Srinivas said:
Hi Dr. Peterson,
I have attached one more image . I am not able to understand what is 692 units between E and D because FE is 310 and the sum is more than FD 881units. As you have worked on these things before please reply if you have time. CD is 43 units not 48.
Click to expand...
I can't read that. And can you explain the different lines? What does the original look like?
 
It is the same figure that i attached yesterday, the only difference is the units of ED is 692( mentioned below the line) and FE is showing 310( above the line ) and the sum of these is more than FD I.e 881 ( in yesterday's document it was 880).
 
Srinivas said:
It is the same figure that i attached yesterday, the only difference is the units of ED is 692( mentioned below the line) and FE is showing 310( above the line ) and the sum of these is more than FD I.e 881 ( in yesterday's document it was 880).
Click to expand...
That doesn't change the fact that it is unreadable, and has extra lines you haven't explained.

1661342899196.png

And I doubt that the changes you describe make it any more likely that it can be constructed, especially if you are saying that F, E, and D are not collinear. That means we'd need even more information.

Are all the numbers you mention actually on the original document, or are some guesses or calculations of your own, as you implied in post #13?

Here is what I think we have:

1661343547954.png

Here I added circles centered at F and D, whose intersection would give point E; there are two possibilities, neither of which works.
 
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