Rent for a DAY: Illustrate TTriangle Area Formula, A= b × h /2, Why
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.
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