Triangle Area Formula, A= b × h /2, Why?

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Triangle Area: Uncovering the Mystery Behind A = b × h / 2 For any given triangle, selecting a base (b) and its corresponding height (altitude) h reveals that the area is precisely b × h / 2. But why does this formula hold true? Without grasping the underlying concept, students often struggle to identify the base and its accompanying height. The truth is, any side of the triangle can serve as the base; once chosen, the height remains fixed. To grasp this concept, consider two identical copies of a triangle being joined together to form a parallelogram. This shape can be easily converted into a rectangle with an area of b × h. So, why must we divide the result by 2? The answer lies in the fact that we're seeking the area of the original triangle, not the combined area of two triangles. It's essential to understand that the formula A = b × h / 2 is rooted in our knowledge of rectangles. Two different explanations can illustrate this process. Regardless of which method you choose, it ultimately comes down to what we know about rectangles. To visualize this concept, two examples are provided below. The triangle chosen for demonstration purposes is arbitrary; feel free to experiment and explore the relationship between A = b × h / 2 on your own.