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hello welcome to my presentation on the in-depth analysis of area now were going to connect the ideas of area to something much more complex in the integral were going to see the area and definition of integral and how it connects later on to its antiderivative for so to begin with we want to start with the most basic of areas and that is in this case with the rectangle so in a basic rectangle as we have learned or as youve learned before the area is just base times height right and I think about this thats one of the most important areas because you can actually derive other area formulas from this one so if you cut in half through its diagonal and if you see what you get you get two equal area pieces in this case they look like triangles your three sides but they are triangles but because you divide the you divide it into two equal pieces its a division of two so the new area of each individual piece as you might have guessed is base times height divided by two one half times b