The polyhedron unit of Geometry begins students on a completely new path in the world of mathematics. At this point, they are asked to begin thinking about things in three dimensionally which can be very challenging at first. Kuta Software offers lots of basic problems to get students in the right frame of mind at the beginning of this Geometry unit. The most important aspect of polyhedrons is being able to identify the different parts that make up the whole shape.
To describe a polyhedron, think of a bedroom will four walls. The four walls are the lateral faces of this polyhedron (this is specifically a cube). The floor and ceiling are the bases of the bedroom. The creases at which the lateral faces meet other faces and the bases are called the edges of the room. The endpoints of these edges are referred to as the vertices of the polyhedron. There are plenty of Geometry tutorials on Youtube that describes this process and draws out the shapes if you learn better with visuals.
There are two different types of areas that can be calculated in our above example. First off, there is the lateral area. This area is just the sum of the areas of the four walls. The formula to calculate this is: Lateral Area = (perimeter of the base)(height of the shape). Often times lateral area is used by food industries when they want to find out how big they need to make a label for their products.
Surface area is the same thing as the lateral area but also includes the area of the two bases. The formula is: SA = (Lateral Area) + (the sum of the area of both bases). It should be quite obvious from this given formula that the surface area value should always be larger than the lateral area. Generally, on standardized tests (such as the ACT) these formulas are given to you. Students are expected to properly apply the formula, knowing very well what each variable symbolizes in their given problem. While the TI-84 graphing calculator will help out quite a bit on a major portion of the ACT, you are mostly on your own in actually understanding how to apply the above formulas.