You can visualize the formula for the area - I guess that's what you mean - as multiplying the height by the average width.You can also derive it more formally, by splitting a typical trapezium into rectangles and triangles.
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There's no specified formula given in the question regarding trapezoids and so therefore it's impossible to answer a question without a question.
Yes
Both trapezoids and rectangles are quadrilaterals.
how are trapezoids and rectangles
parallelograms have two sets of parallel lines trapezoids do not
No.