Geometry for Beginners – Vocabulary for 3D Shapes plus Surface Area and Volume

Welcome to Geometry for Beginners. In this article, we will shift our focus away from two-dimensional figures where we discuss perimeter, area, and the derivations of these formulas. This article introduces the new vocabulary needed for three-dimensional figures, as well as the concepts of surface area and volume. The figure we will use for this article is the prism. Think of a Rubik’s cube or a box of tissues and you have a good mental image of a prism.

Remember that two-dimensional figures have angles, sides, and vertices. Similarly, three-dimensional figures, such as prisms and pyramids, also have “parts”; and this new terminology must be memorized. The 3 tags we need are:

1. faces – The flat surfaces that form the figure. These faces are polygons and there can be different shapes of polygons in the same figure. For a cube, all faces are squares; but a triangular prism has triangles for bases while the remaining faces are rectangles or parallelograms.

2. Borders – Line segments formed where two faces meet.

3. Vertices – The corner points where three faces meet.

We have already mentioned the Rubik’s Cube and a box of tissues as examples of prisms. A cereal box is another good visual image. Prisms have identical polygons as the “top” and “bottom” of the figure, although the figure does not have to be oriented that way. These two identical polygons are called the essential and can be any polygon. The remaining faces are formed by connecting the corresponding vertices at the top and bottom and this forces those other faces, called side faces–be rectangles or parallelograms. If the lateral faces are perpendicular to the bases, the figure is called right prism and the lateral faces are rectangles. If the prism has a “tilt”, which means that the sides are not perpendicular to the bases, the figure is called oblique and the lateral faces are parallelograms.

Note: There are several more new terms in that paragraph, so go back and make sure you understand the meaning of each new term.

Prisms are named both by the shape of the bases and by whether the figure is straight or oblique. The label “right pentagonal prism” should tell you that you have a three-dimensional figure with two bases that are pentagons and the sides are perpendicular to the bases. Also, now you should know that there are 5 side faces, one for each side of the bases, which are all rectangles.

Bail! For right prisms, the length of an edge is also the height If the prism is oblique, the edge is NOT the height and it may be necessary to calculate the actual height.

Now that we have the necessary terminology, we are almost ready to calculate the two important measurements of three-dimensional figures: area Y volume. Think of the image of the cereal box. The box itself is a packaging and represents the concept of surface. This is a very important measure for manufacturers. The cereal inside the box represents the capacity or volume of the cereal box. (We’ll pretend that the cereal boxes are really full when we buy them.)

We will cover the actual formulas for the surface area and volume of various shapes in future articles. Initially, these formulas will seem unusual. However, the good news is that you only need to know the 2-dimensional formulas for area. If you can calculate the area of ​​triangles, squares, rectangles, etc., then you are ready for surface area and volume. If you have weaknesses in these skills, go back and review this material first.