Triangle Area, A= b × h /2, why?

Given any triangle, for a chosen base b and the corresponding height (altitude) h, the area is b × h /2. But why? Without knowing the conceptual foundation, we frequently have students struggling to find the base and the corresponding height. Any side can be the base; once that is chosen, the height is fixed.

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

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

Rafts:

No

Supports:

No

Resolution:

.1 to .2mm

Infill:

5-20%

Post-Printing

Snap the two triangles together and see how they make a parallelogram.

- 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.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU

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