Which formula is used for the area of a trapezoid?

The formula used for the area of a trapezoid is [ A = \frac{1}{2}(B + b)H ], where ( B ) is the length of the longer base, ( b ) is the length of the shorter base, and ( H ) is the height of the trapezoid. This formula calculates the area by averaging the lengths of the two bases and then multiplying by the height, which effectively accounts for the trapezoid's shape that is different from rectangles or parallelograms.

The key idea behind this formula is that a trapezoid can be thought of as a combination of two triangles and a rectangle, and by averaging the bases, it provides a more accurate representation of the trapezoid's area. This is particularly useful in geometry, where understanding various shapes and their corresponding area calculations is fundamental for solving more complex problems involving polygons.

Other formulas listed relate to different geometric shapes or measurements: one pertains to the area of a rectangle, another to the volume of a three-dimensional object, and one incorrectly suggests a formula for calculating the circumference of a circle. Each of these has its own context and application, separate from the area of trapezoids.