Surface Area of Prisms and Cylinders

Every face covering the outside of a solid is added. With the base changing across rectangular prisms and cubes, triangular prisms, trapezoidal prisms, pentagonal prisms, cylinders, prisms with an uneven base and half cylinders, the two bases and the side faces are counted one sheet at a time and added, as calculation.

In a half cylinder, the rounded face and the two semicircular bases get counted while the flat rectangle of the cut face is left out of the answer. Because the shape is a cylinder halved lengthwise, one new flat face has been made. Two rectangles in the opened-out drawing means nothing is missing there.

The same solids whose insides were measured are counted again here from the outside. The footing is the grasp of solids made firm in Volume of Prisms and Cylinders. In Surface Area of Composite Solids the faces that disappear and the faces newly made have to be sorted out.