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Measures Involving Three-Dimensional Figures
Lesson Objective
Now we'll turn our attention to measuring various characteristics of three-dimensional figures. Specifically, we'll
review surface areas and volumes of cones, cylinders, prisms, and other common solids. At the conclusion of
the lesson, we should be able to calculate surface areas and volumes for almost all regular solids.
Previously Covered
A polyhedron is a three-dimensional solid whose faces are polygons.
A prism is a polyhedron that has two parallel, congruent faces called bases. The other faces are
parallelograms.
A pyramid is a polyhedron whose base is a polygon and whose faces are triangles with a common vertex.
Measuring Polyhedra
Surface Area
The surface area of a three-dimensional figure is the sum of the areas of its faces.
Since the faces of a polyhedron are polygons, the surface area of a polyhedron is the sum of the areas of
its polygonal faces.
Let’s look at a prism first. Each of the faces of the rectangular prism below is a rectangle. What is its
surface area?
• The prism has two rectangular faces with dimensions 3 in. x 8 in. Each has
area
• Two faces have dimensions 8 in. x 12 in. Each has area
• Two faces have dimensions 3 in. x 12 in. Each has area
The surface area of the prism is:
