What is the key difference in the formulas for calculating the area of a trapezoid and that of a parallelogram?

The key difference in the formulas for calculating the area of a trapezoid and that of a parallelogram stems from how each shape is defined and the relevant dimensions used in the calculations.

For a trapezoid, the area formula is determined by the lengths of the two parallel bases and the height. It is expressed as:

Area = (1/2) × (base1 + base2) × height.

This formula incorporates the sum of the lengths of the two bases, emphasizing that the area calculation depends on both bases being considered together.

In contrast, the area of a parallelogram is calculated using the formula:

Area = base × height.

Here, there is only one base involved, as both pairs of opposite sides in a parallelogram are equal, meaning there is no need to sum anything. The height remains perpendicular to the base, but there is no additional base to factor into the calculation.

Thus, the distinct use of both bases in the trapezoid formula, versus the use of a single base in the parallelogram formula, highlights a fundamental difference in how the areas of these two geometric figures are calculated.