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Trapezoid/Trapezium Area Formula, A= (a+b) × h /2, why?

3D model description

Trapezoid/Trapezium Area, A= (a+b) × h /2, why?
Given any trapezoid, if the parallel top and bottom are a and b, respectively, and the corresponding height (altitude) is h, the area is (a+b) × h /2. But why?

To see why, we take two congruent copies of a trapezoid and make a parallelogram with the same height and a base of (a+b). Such a parallelogram can be easily converted to a rectangle with a base of (a+b) and height (h, or width), and, accordingly, an area of (a+b) × h. Why do we have to divide that by 2? Well, it is because we want to know the area of the trapezoid. Of course, there are other ways to explain it. One way or the other, it goes back to what we know about rectangles or other shapes.

Two versions are provided to demonstrate the process behind A= (a+b) × h /2. The trapezoid is just a random one. Have fun.

3D printing settings






.1 to .2mm



  • 3D model format: STL


STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

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