Trapezoid problem

[Loki123]

I have come across a problem where you are given base one, base two, diagonal one and diagonal two of a trapezoid. The task is to calculate the surface, in other words, you need to find the height. I did it with pythagoras, although not difficult, this problem had big numbers, over 100 each which made squaring and other operations quite problematic. Any other, simpler, ways to solve this?

 

[pka]

To Loki123, if you continue to post half-posed questions( incomplete) questions you are going to not get help that you need.
Look at this post. You are using vocabulary that has no western equivalate. I suppose that by surface you mean area.
The letter P has no meaning in this context. Thus you must tell us what you mean by the terms that you use.
If the question is simply What the the area of the trapezoid?
The answer is $h\cdot\left(\dfrac{a+b}{2}\right)$: one half the sum of the lengths of the bases times the height.

 

[Loki123]

To Loki123, if you continue to post half-posed questions( incomplete) questions you are going to not get help that you need.
Look at this post. You are using vocabulary that has no western equivalate. I suppose that by surface you mean area.
The letter P has no meaning in this context. Thus you must tell us what you mean by the terms that you use.
If the question is simply What the the area of the trapezoid?
The answer is $h\cdot\left(\dfrac{a+b}{2}\right)$: one half the sum of the lengths of the bases times the height.

Sorry, english is not my first language, I thought surface and area could be interchangable here. See what P equals to, that's what it stands for.

 

[BigBeachBanana]

I thought surface and area could be interchangable here.

Surface area refers to 3-D shapes. For 2-D, it's just area.

I don't understand what's given and what's missing from your diagram. You have a,b, and h. You have enough info to find the area.

 

[pka]

Sorry, english is not my first language,

That is well & good. But this is a English language forum. Thus you should get someone to help you with translations.

 

[Loki123]

Surface area refers to 3-D shapes. For 2-D, it's just area.

I don't understand what's given and what's missing from your diagram. You have a,b, and h. You have enough info to find the area.

I wrote it in the beginning. I have a, b, d1 and d2.

I have come across a problem where you are given base one, base two, diagonal one and diagonal two of a trapezoid.

 

[Loki123]

That is well & good. But this is a English language forum. Thus you should get someone to help you with translations.

I'll try to research terms before from now on.

 

[BigBeachBanana]

In your diagram, draw 2 additional triangles like below: DPA and BQC

 

[Dr.Peterson]

I have come across a problem where you are given base one, base two, diagonal one and diagonal two of a trapezoid. The task is to calculate the surface, in other words, you need to find the height. I did it with pythagoras, although not difficult, this problem had big numbers, over 100 each which made squaring and other operations quite problematic. Any other, simpler, ways to solve this? View attachment 30596

Can you show us the details of your work? What you say sounds reasonable, but there may well be steps that you can do more efficiently.

By the way, pka is right that defining P would have been helpful, since to us it sounds more like "perimeter"; but I have no trouble understanding "surface", having worked with many students whose English is weak (some of them not even Americans ). However, he could be a lot kinder, and is not representative of all English-speakers.

 

[blamocur]

I have come across a problem where you are given base one, base two, diagonal one and diagonal two of a trapezoid. The task is to calculate the surface, in other words, you need to find the height. I did it with pythagoras, although not difficult, this problem had big numbers, over 100 each which made squaring and other operations quite problematic. Any other, simpler, ways to solve this? View attachment 30596

Since you've found $e$ and $h$ you must have solved the problem -- what kind of help do you need? Do you want to post your full solution?

 

[Loki123]

Since you've found $e$ and $h$ you must have solved the problem -- what kind of help do you need? Do you want to post your full solution?

I would just like to know if there is a simpler way to solve this because it gets complicated this way with big numbers. I'll post the full solution.

 

[Loki123]

Can you show us the details of your work? What you say sounds reasonable, but there may well be steps that you can do more efficiently.

By the way, pka is right that defining P would have been helpful, since to us it sounds more like "perimeter"; but I have no trouble understanding "surface", having worked with many students whose English is weak (some of them not even Americans ). However, he could be a lot kinder, and is not representative of all English-speakers.

Here it is. However, I did this from memory, because of some circumstances I cannot seem to find the original problem but this is 99% like it. Some number might be off. It gets really exhausting with all this multiplying and leaves a lot of room for mistakes so I was wondering is there a way to do it without squaring so much.

 

[Dr.Peterson]

View attachment 30609
Here it is. However, I did this from memory, because of some circumstances I cannot seem to find the original problem but this is 99% like it. Some number might be off. It gets really exhausting with all this multiplying and leaves a lot of room for mistakes so I was wondering is there a way to do it without squaring so much.

I can look at more details later, but the usual way to avoid numerical exhaustion is to avoid actual numbers until the end. Keeping everything as variables is standard practice; you end up with a formula into which you can plug the numbers.

This one may be complicated enough that the formula will be ugly, and you may not want a single formula, but multiple steps.

 

[BigBeachBanana]

The dimensions in your diagram must be wrong. I'm getting a solution of h=0 and e=10. The two equations are circles with a tangent point at (0,10).
$$110^2=h^2+(100+e)^2 --(1)\\ 160^2=h^2+(170-e)^2--(2)$$

 

[blamocur]

View attachment 30609
Here it is. However, I did this from memory, because of some circumstances I cannot seem to find the original problem but this is 99% like it. Some number might be off. It gets really exhausting with all this multiplying and leaves a lot of room for mistakes so I was wondering is there a way to do it without squaring so much.

You switch from "-340e" to "-300e" at some point for no apparent reason.

 

[Loki123]

The dimensions in your diagram must be wrong. I'm getting a solution of h=0 and e=10. The two equations are circles with a tangent point at (0,10).
$$110^2=h^2+(100+e)^2 --(1)\\ 160^2=h^2+(170-e)^2--(2)$$

I don't know the actual numbers of the problem since I am currently in no position to check them so I went off my memory which could have a number or two off a little. That's why I didn't post it with actual numbers at first. I am more interested in the method and that's what I am asking for. I'll do the calculating when I get ahold of the problem.

 

[Dr.Peterson]

I don't know the actual numbers of the problem since I am currently in no position to check them so I went off my memory which could have a number or two off a little. That's why I didn't post it with actual numbers at first. I am more interested in the method and that's what I am asking for. I'll do the calculating when I get ahold of the problem.

Your work is essentially what I did. PLEASE do what I suggested and use variables only; you'll get a complicated expression for e, which you can evaluate for specific numbers, and then use the result to find h. I don't think there will be a method that involves less squaring, unless you obtain a formula and are able to simplify it.

But the numbers you used in the example are wrong (they do lead to h=0 even when I try drawing it), and you made numerical errors in your work.

You might want to test your method with smaller numbers (perhaps derived by knowing h in the first place), and use that to check your formula.