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Trapezoidal Base
The two-dimensional, or flat, shape called a trapezoid qualifies as a quadrilateral or quadrangle, because it consists of four sides and four angles. Because those sides and angles form a closed shape, it is also considered a polygon. What defines the trapezoid, however, is that one pair of opposite sizes are parallel to each other. These sides may measure any length, and the other two sides may form any angle or length. In the case of an isosceles trapezoid, the two sides that are not parallel mirror each other; they are the same length and form same-size angles. The isosceles trapezoid may resemble an isosceles triangle with its top point cut off by a line that is parallel to the triangle's base.
Triangular Sides
Although the base of a trapezoidal pyramid is quadrilateral, four triangles form the sides of the pyramid. These triangular sides slant inward, with their top points all meeting at a single point: the apex, or peak of the pyramid.
Pyramid
Each pyramid is named after the shape of its base. Therefore, a square pyramid has a square base, while a trapezoidal pyramid's base is shaped like a trapezoid. If the apex of the pyramid does not align with the center of the base, the pyramid is also considered an oblique pyramid; if the apex does line up with the base's center, then the pyramid is considered a right pyramid. Regardless of type, a pyramid's volume equals third of the area of the base, times the height of the pyramid.
Trapezoidal Pyramid
The trapezoidal pyramid is considered an irregular pyramid, because the four sides and four angles of its base shape -- a trapezoid -- are not equal to each other. The only regular quadrilateral pyramid is a square pyramid. In the case of a truncated trapezoidal pyramid, the pyramid's apex has been shaved off by a plane that is parallel to the base. This altered shape possesses six trapezoid-shaped sides.