The Question of why?

When I was in the 5th or 6th grade we started to learn about area. We first learned about the area of a rectangles and came up with the formula of (LXW=AREAsqr). When we moved on to triangles the teacher asked us how would we find the area, I thought it would be the same concept as the rectangle but then I realized that the triangle has three sides so how would the formula (LXW=AREA sqr)work. She gave us all a rectangular piece of paper, we were to make a doted line from one diagonal to the next, then fold the paper along the doted line and cut it. We saw that we had two identical triangles, she asked us to put it back together and find the area of the rectangle. After we found the area of the rectangle, we took it apart again she asked if the area of the each of the triangle is the same as the rectangle, no the area of the triangle is now half the rectangle.  So she let us make up our own formula for the area of a triangle based on what we just discovered. That is how i acme to understand why the area of a triangle is (1/2BXH).

The questions i would like to know why is.

Why is it that the answer is different when we switch from degrees to radians.  I found his question interesting because it was never explained to me why I had to make that change when doing calculus and what is the difference between to the two, I was just told that’s what is done.

Why does the quadratic formula works. I saw it in the examples and it made me think that I have no idea why it works I just know how to use it.


2 thoughts on “The Question of why?

  1. Hi Latina,

    Congratulations – you’ve been the first to create your own post on our site (it wasn’t my intention with this assignment, but it’s just fine- and I’ll be assigning this kind of thing to the whole class later on, so you have a headstart).

    The formula for the area of a triangle is a great example of something students can discover on their own once they know the area of a rectangle – what’s nice is that it gives you a way to figure out the formula if you ever forget it (I tend to be bad at remembering formulas, but relatively good at remembering where they come from…).

    -Prof. Reitz

    1. I’m fortunate that I had the opportunity to discover this formula myself and see how it works and understand how to apply it. How I could teach this to my future students and have them make the same discovery I did.

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