No, the formula for a trapezoid's area is (base1 +base2)x height divided by 2, so the bases are only part of the total area.
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Which solid?? For the same height, larger area of base = larger volume. So they are directly related.
formula of the volume of a prism = (base area)(height) formula of the volume of a pyramid = (1/3)(base area)(height) therefore, to convert the volume of a prism to that of a pyramid, just divide it by 3
They would have to have the same base area, if that's what you mean.
Yes
There is no reason for the surface area to remain the same even if the volume is the same.