What is the area of a trapezoid?

The area of a trapezoid is found by taking the average of the lengths of the two parallel sides, known as the bases, and then multiplying that average by the height of the trapezoid. This is represented by the formula ((1/2) × (Base_1 + Base_2) × height).

This formula is derived from the principle that the area of a trapezoid can be thought of as the area of a rectangle and two triangles combined. The two bases of the trapezoid are the top and bottom edges that are parallel, and the height is the perpendicular distance between these bases. By averaging the lengths of the two bases, you determine the 'effective' base length over which to calculate the area of the shape.

In more detail, if you think of the trapezoid as being made up of a rectangle that connects the two bases along with the two triangular sections that taper off, the average of the bases provides the correct scaling for finding the collective area above and below this central rectangle over the height of the trapezoid.

Thus, the formula correctly accounts for the unique geometry of the trapezoid, where the bases can be of different lengths, hence why option C, which utilizes the average