Volume of Prisms and Cylinders

Finding the ground the base covers and then multiplying by the height carries the whole lesson. The base changes across rectangular prisms and cubes, triangles, trapezoids, rhombuses, and the pentagon of a roof shape joining a triangle to a rectangle, then a hexagon, then a prism whose dented base is found by adding and subtracting, and on to cylinders and half cylinders standing upright and lying down, all as calculation. One word problem about a tank or a can is attached.

The height used for the base area is the inner dashed line drawn perpendicular to the base, marked with a right angle. In a prism whose base is a parallelogram, that gets missed and the slanted side length, which has no business in the area, is taken into the expression. Trace with a finger which figures on the drawing were picked up.

The ground that had been found as an area now carries the role of a base. Into Volume of Composite Solids, which starts from choosing whether to split or to hollow out, this way of finding a base is carried straight over.