How to get the right volume in a trapezoid box?

Hello all :D,

I have been working on a trapezoid design for 1 year now for my speakers and well it's not a new box desing to anyone it's my own design. Is there a easy way to figure out the volume for the inside of a trapezoid box? Here's a example. If the front and back of the box is 9 inch's on the bottom and 6 Inch's on top. Now for the the side's of the box. The bottom is 7 inche's on the bottom and 4 inch's on the top. So again how can I find the cubic feet inside this box? Well again thank you for all you help it's just I am new to this trapezoid box designing. Thanks Jm
 
Depends of course on how tall the box is which you did not specify. I think the basic formula is very simple: take the average area of the top and bottom faces and multiply by the height. So it sounds like the base is 6in x 9in = 54in^2 and top is 4in x 7in = 28in^2. Average area is (54in^2+28in^2)/2=41in^2. Let's assume the height is 12in. So 41in^2 x 12in = 492 in^3.
 
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How the heck can we get so close but be different there X?
(6+9)/2=7.5
(4+7)/2=5.5

7.5x5.5x12=495 in^3
495/1728=0.286 ft^3

Based on ID of 12"

Why are you averaging the dimensions of each face? If you take the extreme example of a trapezoid that is straight like a regular rectangular box say 6x9x12, we would get doing it your way (6+9)/2=7.5 and 7.5x7.5x12= 675. Whereas the true vol is 54x12= 648.

I just think about it from a limits point of view as the area has to be the average between the two extremes of a rectangular box 6x9x12 and 4x7x12.
 
Cal & X fighting over the use of the Associative property.
Associative property, really?
take the average area of the top and bottom faces and multiply by the height. So it sounds like the base is 6in x 9in = 54in^2 and top is 4in x 7in = 28in^2.
Is that what you get from the dimensions in post 1?
 
Has everyone actually forgotten there basic geometry? Cal, glad someones brain still works here and you go that right. Why would you have to use a cad program to figure this out? That is like asking what the area of a circle is! Now if we start talking about the sq. rt of -1 I imagine that many would not know the term i, but a simple trapezoid you could look that up on Google in two seconds. How do you do ac circuit work if you don't remember some basic math?
 
Associative property, really?

Is that what you get from the dimensions in post 1?

I think we are on same thinking. Without a picture I interpreted trapezoid in the vertical dim with top wall and bottom wall being rectangular csa. I think you see this as a trapezoid csa on top and bottom wall of varying area - trapezoid in all dimensions. Not clear what op meant based on words. That's why we have diagrams. We are both right. Depends on interpretation. Heck op did not even give height. My formula of average areas on top and bottom multiplied by height applies to any cross section, round, trap, triangle, etc. As long as same type of cross section top and bottom.
 
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