When Arthur is at a birthday party, he enjoys sorting the gifts by their different shapes as a strategy to help him guess what is inside each package. He observes the similar and different attributes of the gifts to put them into categories. Looking at the characteristics of the gifts, what are the shapes of the sides of each gift, and how many sides, edges, and corners does each have?

In this concept, you will learn how to classify three-dimensional solids according to their common attributes.

### Classifying Solid Figures

Solid figures are three-dimensional objects, meaning they have length, width, and height. Because they have three dimensions, they have depth and take up space in our universe. Solid figures are identified according to the features that are unique to each type of solid. Specifically, you can observe the numbers of **faces,** **edges,** and **vertices,** as well as the shape of the **base**.

The flat surfaces of a solid figure are its **faces**, or sides as they are commonly called. The **base** is the face on which the figure rests. The **edge** of a solid figure is the line segment where two faces meet. A **vertex** (plural: vertices) is the corner that is formed where the ends of the line segments of two or more faces meet.

A **sphere** is a solid figure that has no faces, edges, or vertices. This is because it is completely round; it has no flat sides or corners.

A **cone** has one face, but no edges or vertices. Its face is in the shape of a circle. Because a circle is a flat, plane shape, it is a face. But because it is round around the outside, it does not form any edges or vertices.

A **cylinder** has two circular faces but also no edges or vertices.

A **pyramid** has one base and at least three triangular faces. It has edges where faces meet each other or the base, vertices where two faces meet the base, and a vertex at the top where all of the triangular faces meet. A pyramid is named by the shape of its base.

A triangular pyramid has a triangle-shaped base and three other triangular faces, or four in all.

A rectangular pyramid has a rectangle-shaped base and a square-based pyramid has a square-shaped base. They both have four triangular faces, five faces in all.

Rectangular Pyramid Square Pyramid

A **prism** is a solid figure that has two congruent parallel faces and any number of sides. In other words, it can have any number of faces, but at least two of them must be parallel. The shape of the two parallel faces can be a triangle, square, rectangle, pentagon, hexagon, or any other kind of polygon. Prisms are named by the shape of their bases. Here are three examples of different prisms:

is a prism where all the faces are square.**cube**A

**Examples**

#### Example 1

Earlier, you were given a problem about Arthur and his gift reorganization.

Arthur needs to figure out the characteristics of two gifts. He also wants to characterize the big round helium balloons.

Arthur considers the first present, a large blue one.

First, it has 6 faces.

Next, they are all square including the base.

Then, the gift has 8 vertices and 12 edges.

The answer is that the large blue present is a cube.

Arthur goes on to consider the smaller present.

First, it has 6 faces.

Next, all of the faces are rectangles.

Then, the present has 8 vertices and edges.

The answer is that the gift on the left side of the table with the dark blue bow is a rectangular prism.

Finally, Arthur considers the balloons.

First, they do not have faces.

Next, they do not have edges or vertices.

Then, they are completely round.

The answer is that the balloons are spheres.

#### Example 2

Identify the figure below. Be as specific as you can.

First, the figure has 7 faces. Five of the faces are rectangles; 2 of the faces are pentagons which are parallel and congruent.

Next, the base is a pentagon.

Then, there are 15 edges and 10 vertices.

The answer is the solid figure is a pentagonal prism.

#### Example 3

Identify the figure.

First, the figure has 4 faces, all triangular in shape including the base.

Next, there are 6 edges and 4 vertices.

Then, 3 of the triangles form a vertex at the top.

The answer is the solid figure is a triangular pyramid.

#### Example 4

Identify the figure.

First, the figure has 1 face.

Next, the face is in the shape of a circle.

Then, it does not have any edges or vertices.

The answer is the solid figure is a cone.

#### Example 5

Identify the figure.

First, the figure has 6 faces.

Next, all of the faces are square including the base.

Then, there are 8 vertices and 12 edges.

The answer is the solid figure is a cube.

#### Example 6

Identify the figure.

First, this figure does not have any faces.

Next, this figure does not have any edges or vertices.

Then, this figure is completely round.

The answer is the solid figure is a sphere.

### Review

Identify each figure. Be as specific as possible.

Look at each picture and determine whether each is a prism, pyramid, cylinder, cone or sphere.

### Review (Answers)

To see the Review answers, open this PDF file and look for section 10.1.