The subject of this chapter is the measurement of the areas of subsets of the plane
. The areas of elementary geometric figures, such as squares, rectangles, and triangles, are already known to us. By
known to us
we mean that, for example, by defining the area of a rectangle to be the product of the lengths of its sides, we obtain quantities agreeing with our intuition. Because every right-angle triangle is half a rectangle, the areas of right-angle triangles are also known to us. Similarly, we can obtain the area of a general triangle.