When calaculating area why do you use lxw for rectangles and bxh for parrelelograms?

Answer 1

Your question cuts to the heart of the matter. We need to stop confusing kids in math. The simple truth is that ALL area formulas should be BASE x HEIGHT (yes, including quadrilaterals). It's a matter of perspective and that is what we should be teaching our kids. I'll explain:

Think of a any rectangle as the 2-D front face of a 3-D building extending into the drawing. With that perspective in mind, length and width to find area makes no sense but base and height make perfect sense. Now change your perspective: visualize that a drone is sent up above the building looking down with its camera. Do you see the same rectangle? Yes, but now finding area using base and height makes no sense but length and width do. See? Perspective is everything and, convenientlyand tragically, left out of area discussions at all levels.

Now take other quadrilaterals like parallelogram and trapezoid. Why is their area formula base x height? Is it because there is some weird unwritten rule that all rectangles and squares are top-down views of a prism and parallelograms and trapezoids are front-facing views of those prisms? Do we not see how confusing math is to kids by our own design (laziness)?

Circling back to an answer for you: it is time to unify. I suggest making all dimensions in area discussions BASE x HEIGHT. This already matches traingles, parallelograms, trapezoids, etc. and the terminology reinforces volume work as the labelling is the same. The only thing that needs to change is telling students that rectangles and squares they look at are the perspective of a front face of a building (take them outside and look at any nearby building). With this small perspective clarification students can now use base and height for all area volume formulas, the nuance now being how each formula uses base and height to find the area. The ensuing depth of discourse is worth every penny And that is why this is just my two cents!

Answer 2

you tell me