Yes because if you square root the area of a trapezoid that will give you the side of a square
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No.
Yes, certainly. The trapezoid area is one half sum of bases times height and the parallelogram area is base times height If the base of the parallelogram is equal to 1/2 the sum of he trapezoid bases, they have the same area
of course base times height for a square or rectangle. but for a trapezoid a= h x "b1+b2"
A parallelogram and a trapezoid are a couple of examples.
Yes. The term "surface area" as normally used for 3-dimensional objects but that does not alter its meaning. The two measures are the same.