Video narration
How can a triangle's area come from a rectangle you already know how to measure? Imagine Nivan looking at a sheet of paper, split corner to corner by a diagonal. You see two triangles, each covering the same amount of paper. The whole rectangle's area is the area of triangle one plus triangle two. The diagonal makes them equal: one triangle is half its corresponding rectangle. The paper rectangle's area is base multiplied by perpendicular height. That height meets the base at a right angle; it is not simply the sloping edge. Take half the rectangle's area, and you have the triangle's area. Check on a square grid: count the squares in the whole rectangle, then compare one shaded triangular half. It covers half as much. So, on Nivan's paper, one triangle is half its rectangle. Its area is one-half times base times perpendicular height.