Similar trapezoid bases ratio question

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rbq10

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ejkaminsky said:
Ina trapezoid the parallel sides are in the ratio k:1 where k>1. The line segment joining the midpoints of the non-parallel sides divides the trapezoid into two regions whose areas are in the ratio 5:2. What is the value of k?

A) 12
B)5/2
C)13
D)25/5
E)7

Let a = the short parallel side and ka = the long side.

Then, a(k+1)/2 = the median (the average of the two parallel sides).

The larger area A1 = [ka + a(k+1)/2]/2 = a(3k+1)/4

The smaller area is A2 = [a + a((k+1)]/2

Dividing a1 by a2 yields (3k+1)/(k+3) = 5/2

I suspect you can take it from here.
Click to expand...

Hi there,
I'm having trouble with a similar question and was wondering you can point me in the right direction. I have a trapzoid with the one side angle at 67 deg and the other at 72 deg. The height of the trapezoid is 40. Is it possible with this amount of information to calculate the ratio of the bases, assuming 'a' is the short base and 'ka' is the longer of the two bases?
 
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rbq10 said:
I have a trapezoid with the one side angle at 67 deg and the other at 72 deg. The height of the trapezoid is 40. Is it possible with this amount of information to calculate the ratio of the bases, assuming 'a' is the short base and 'ka' is the longer of the two bases?
Click to expand...

Yes, in terms of a. Like (a+25)/a, for example, where a+25=ka.

Using right-triangle trigonometry is one way.

Do you have any more information about the trapezoid, other than the height and the angle measurements? Which ratio is 'the ratio'?



Cheers :cool:
 
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Re:

mmm4444bot said:
Yes, in terms of a. Like (a+25)/a, for example, where a+25=ka.

Using right-triangle trigonometry is one way.

Do you have any more information about the trapezoid, other than the height and the angle measurements? Which ratio is 'the ratio'?



Cheers :cool:
Click to expand...

Thanks for the help. This is for a rough calculation for a trapozoid prism where the only additional information I have (other than what I already mentioned above) is the area on top of the trapozoid.
Unfortunately I don't know what the length and width values which make up the area on top, so I am wondering if I can calculate the base area using some type of a ratio.

Sorry if my explanations aren't too clear :(
 
I don't think you have enough information, for a unique solution..

A known rectangle area does not define the rectangle's dimensions because there are many different rectangles having the same area.

You could assign a symbol for the width of the prism (i.e., the distance from one trapezoidal surface to the other). Then, solutions for the prism could all be expressed in terms of that symbol.
 
Re:

mmm4444bot said:
I don't think you have enough information, for a unique solution..

A known rectangle area does not define the rectangle's dimensions because there are many different rectangles having the same area.

You could assign a symbol for the width of the prism (i.e., the distance from one trapezoidal surface to the other). Then, solutions for the prism could all be expressed in terms of that symbol.
Click to expand...

Hmmm.. Thought so. Thanks again for helping me out :D

The reason why I was hoping to get a ratio is because ultimately my main aim is to estimate the volume of material coming down from a cliff face. The problem is that the only set of information I have (apart from the angles and height) is the area on top which has an undefined shape to it since it is the sum of areas measured from a map that I have drawn.

Since it is an estimation I made an initial calculation assuming that it was in the shape of a parallelogram prism assuming both angular sides are 67 degrees and that the top area = base area.
I'm just wondering how much of a difference would the 5 degrees be to the total volume, hence this attempt int trying to determine in some way the base area of a trapezoidal prism where one side is 5 degrees steeper than the other.

Any suggestions?
 
rbq10 said:
Hi there,
I'm having trouble with a similar question and was wondering you can point me in the right direction. I have a trapzoid with the one side angle at 67 deg and the other at 72 deg. The height of the trapezoid is 40. Is it possible with this amount of information to calculate the ratio of the bases, assuming 'a' is the short base and 'ka' is the longer of the two bases?
Click to expand...

If the top (short side) is 'a' and both the angles you are defining is on the larger side(b) then:

b = h*cot(67°) + h*cot(72°) + a

As you can see that from this equation there is no-way to find "b/a", without some other information.
 
I don't have any more suggestions; you may be trying to model something that has too many unknown factors for even a rough estimate.
 
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