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The area of a trapezium is calculated using the formula that incorporates the lengths of the two parallel sides as well as the height (d) of the trapezium. The correct formula is:

Area = 1/2 (a + b) d

In this formula, a and b represent the lengths of the two parallel sides, and d is the distance (height) between them. This formula works because it essentially averages the lengths of the parallel sides (a and b) and then multiplies this average by the height (d) to give the space contained within the trapezium.

To further clarify, the factor of 1/2 accounts for the fact that we are averaging the lengths of the two bases; thus, this ensures that we are calculating the area accurately based on their respective lengths and the height of the trapezium.

In contrast, the other options do not accurately reflect the geometrical principles required to calculate the area of a trapezium. For instance, simply multiplying the lengths of the sides (ab) or adding them together (a + b) does not take into account the height or the nature of a trapezium's shape, which includes the aspect of height in its area calculation. Multip