Just to add an anecdote about rote memorization -- not one teacher or textbook explained the "why" behind the area of a triangle being base times height divided

Just to add an anecdote about rote memorization -- not one teacher or textbook explained the "why" behind the area of a triangle being base times height divided by two. Just had to memorize that along with everything else. It wasn't until years later I saw something online that showed two right triangles stacked on top of each other forming a rectangle. And then further illustrations on how you could bisect triangles of other shapes to make two right triangles that you could double up to make rectangles. Then it was obvious why you had to take the formula for a rectangle's area and divide it by two for triangles. Similar visualizations are useful for other shapes too. But for some reason (unless I spaced out during that lesson) this was never brought up in any high school or college math class.