This document contains notes from lessons on calculating the areas of triangles. It discusses how the area formula for right triangles can be derived by viewing a right triangle as half of a rectangle. It then explains that the area formula works for all triangles by constructing an altitude to split any triangle into two right triangles. The altitude is defined as the perpendicular segment from a vertex to the opposite side. Examples are given of finding the altitude in different cases. Students are asked to justify relationships between triangle and rectangle area formulas and how to determine the base and height of non-right triangles.