- Characteristics of a Trapezoidal Prism
- 1- Drawing a trapezoidal prism
- 2- Properties of a trapezoid
- 3- Surface area
- 4- Volume
- 5- Applications
- References
A trapezoidal prism is a prism such that the polygons involved are trapezoids. The definition of a prism is a geometric body such that it is formed by two equal and parallel polygons and the rest of their faces are parallelograms.
A prism can have different shapes, which depend not only on the number of sides of the polygon, but on the polygon itself.
If the polygons involved in a prism are squares, then this is different from a prism involving rhombuses for example, even though both polygons have the same number of sides. Therefore, it depends on which quadrilateral is involved.
Characteristics of a Trapezoidal Prism
To see the characteristics of a trapezoidal prism, one must begin by knowing how it is drawn, then what properties the base fulfills, what the surface area is, and finally how its volume is calculated.
1- Drawing a trapezoidal prism
To draw it, you first need to define what a trapezoid is.
A trapezoid is a four-sided irregular polygon (quadrilateral), such that it has only two parallel sides called bases and the distance between their bases is called the height.
To draw the straight trapezoidal prism, you start by drawing a trapezoid. Then, a vertical line of length "h" is projected from each vertex and finally another trapezoid is drawn such that its vertices coincide with the ends of the lines previously drawn.
You can also have an oblique trapezoidal prism, whose construction is similar to the previous one, you just have to draw the four lines parallel to each other.
2- Properties of a trapezoid
As stated before, the shape of the prism depends on the polygon. In the particular case of the trapezoid we can find three different types of bases:
-Rectangle trapezoid: is that trapezoid such that one of its sides is perpendicular to its parallel sides or that it simply has a right angle.
-Isosceles trapezoid: it is a trapezoid such that its non-parallel sides have the same length.
Scalene trapezoid: it is that trapezoid that is not isosceles or a rectangle; its four sides have different lengths.
As can be seen, according to the type of trapezoid used, a different prism will be obtained.
3- Surface area
To calculate the surface area of a trapezoidal prism, we need to know the area of the trapezoid and the area of each parallelogram involved.
As can be seen in the previous image, the area involves two trapezoids and four different parallelograms.
The area of a trapezoid is defined as T = (b1 + b2) xa / 2 and the areas of the parallelograms are P1 = hxb1, P2 = hxb2, P3 = hxd1 and P4 = hxd2, where “b1” and “b2” are the bases of the trapezoid, “d1” and “d2” the non-parallel sides, “a” is the height of the trapezoid and “h” the height of the prism.
Therefore, the surface area of a trapezoidal prism is A = 2T + P1 + P2 + P3 + P4.
4- Volume
Since the volume of a prism is defined as V = (polygon area) x (height), it can be concluded that the volume of a trapezoidal prism is V = Txh.
5- Applications
One of the most common objects that are shaped like a trapezoidal prism is a gold bar or the ramps used in motorcycle racing.
References
- Clemens, SR, O'Daffer, PG, & Cooney, TJ (1998). Geometry. Pearson Education.
- Garcia, WF (sf). Espiral 9. Editorial Norma.
- Itzcovich, H. (2002). The study of figures and geometric bodies: activities for the first years of schooling. Noveduc Books.
- Landaverde, F. d. (1997). Geometry (reprint ed.). Editorial Progreso.
- Landaverde, F. d. (1997). Geometry (Reprint ed.). Progress.
- Schmidt, R. (1993). Descriptive geometry with stereoscopic figures. Reverte.
- Uribe, L., Garcia, G., Leguizamón, C., Samper, C., & Serrano, C. (sf). Alpha 8. Editorial Norma.