Geometric Formulas
The Formula for Areas of Trapezoids
In order to develop the formula for a trapezium it is important to note that a trapezoid is a quadrilateral characterized by a pair of opposite sides running parallel to each other. When referring to trapeziums the parallel sides are referred to as bases, while the opposite sides intersecting the parallel sides upon extension are referred to as legs (Beckmann, 2013).
Therefore, in order to determine the area of a trapezoid, one must rely on the two main components of the trapezoids such as heights and their bases (Van de Walle et al., 2013). Thus, developing the formula for the area of a trapezium it is necessary to consider that, this is given by a half of the trapezium’s height multiplied by the sum of the trapezium’s lengths of the bases which is expressed in terms of the equation shown below:
In the above equation A is the area of the trapezoid, h is the height, and b1 and b2 are the two bases’ lengths as shown in the figure below:
The figure shown above represents the trapezoid bases and height which are required for the determination of the area.
As shown by the above equation which is used to calculate the area of a trapezium, it is necessary to note that this equation is developed as shown in the procedure indicated below:
As in the case of a true triangle, two copies of a trapezoid are likely to be fitted together to form a parallelogram where the height of both the parallelogram and the trapezoid are the same; whereas the base is considered to be the sum of the two parallel sides of the trapezoid. This implies that the area of a parallelogram is given by its height x (base1 + base2) meaning the area of a parallelogram is usually the sum of two bases of the trapezoid; whereas the trapezoid’s height is divided by half.
References
Beckmann, S. (2013). Mathematics for elementary teachers with activities, (4th ed.). Boston, MA: Pearson.
Funbrain, (n.d.) Shape surveyor geometry game. Retrieved January 24, 2014, from http://www.funbrain.com/poly/index.html
Interactivate, (n.d.). Shape explorer. Retrieved on January 24 2014 from http://www.shodor.org/interactivate/activities/ShapeExplorer
Laureate Education, (2013). Area and perimeter [Video file]. Retrieved on January 24 2014 from https://class.waldenu.edu
Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson.
Last Completed Projects
| topic title | academic level | Writer | delivered |
|---|