What is the area formula for a trapezoid when you know the height and the lengths of the parallel sides?

The formula for the area of a trapezoid is derived from the concept of averaging the lengths of the two parallel sides (often referred to as the bases) and then multiplying that average by the height of the trapezoid. In the case of option B, the expression is 1/2 x (side A + side B) x height.

To break this down:

1. The sum of the lengths of the parallel sides (side A and side B) generates the combined lengths of both bases.

2. Averaging these lengths gives a representation of how far apart these sides are, effectively capturing the typical width of the trapezoid.

3. Multiplying this average by the height provides the perpendicular distance between the bases, accurately calculating the area contained within the trapezoidal shape.

This method aligns with the geometric principles of how area is determined for shapes with varying widths. Therefore, option B correctly captures the formula for finding the area of a trapezoid when the height and lengths of the parallel sides are known.