Joshua H.

asked • 04/08/20

I've tried to solve this so many times and can't seem to get it.

A farmer feeds his horses a trough full of corn every day. The trough is in the shape of a trapezoidal prism. The

trough’s base is 1 foot by 4 feet, the height is 1 foot, and the top edge is 1.5 feet by 4 feet. What is the volume of the trough?

Stanton D.

Hi Joshua, So the prism is 4 feet long, at all points; in respect to the trapedoidal crosssection, it is 1.5 ft top, and 1 ft base. That's 1.25 ft average, and it's 1 ft high. So the crosssectional area is 1.25 ft^2, and the volume is 4 times that, or 5 ft^3 . Note that I've "mentally" applied a formula already -- the average width is (1/2) of the sum of the top and bottom widths. If you draw a trapedoid (please do so, to convince yourself!), and cut it horizontally at the middle, then drop and raise perpendiculars from the cut edge points, you will see how the "average" works out as a visual thing: the "extra" "outside" little triangles and being used to "fill in" the "inside" triangle areas on each side. -- Cheers, -- Mr. d.
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04/09/20

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Martin S. answered • 04/09/20

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It would be nice to use a diagram to explain this, but hopefully this will do.


If you were to look at the trough from the right or left end it would look like a trapezoid. the length of the trough is constant (4 feet), and the height of the trough is also constant (1 foot). You can use the formula base times height = volume to get the volume of the trough by using the trapezoid as the base. Multiply the area of the trapezoid by the length and you will have the volume.In this case the height of the trough will be the height of the trapezoid.

The area of a trapezoid is the average of the two bases times the height. The two bases are 1 foot and 1 1/2 feet, so the average of the bases is 1 1/4 feet. Multiply that by 1 foot, and the area of the trapezoid (the sides of the trough) is 1 1/4 square feet. Now multiply that by the length of the trough to get the volume.


4 feet (length) x 1 1/4 square feet (base) = 5 cubic feet.


Hope this helps

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