10.13: Faces, Edges, and Vertices of Solids
Have you ever been to a craft store?
Instead of quilting, Jillian and her mother went to the craft store after dinner. Jillian wanted a new box to use as a jewelry box.
"I'll get the box and then decorate it," she told her mother.
Jillian found the following box at the craft store.
"This cube is perfect," Jillian said putting into her basket.
The cube, like all solid figures is made up of different parts. Do you know what those parts are?
In this Concept, you will learn how to identify the different parts of a solid figure. Then we will come back and identify the parts of the cube.
Guidance
In the last Concept, you learned to identify different types of solid figures. We referred to the “sides of the figure” and to the “bases of the figure.” Well, there are different parts of each solid and knowing the names of these parts can help us with identifying them.
Three Parts of a Solid
- Faces
- Edges
- Vertices
These three parts are relevant to any solid that has flat surfaces, places where flat surfaces intersect and places where planes intersect.
Let’s define each part.
Face – any flat surface
The flat surface that makes the front of this cube is called a face. Many solid figures have more than one face.
Edge – The line segment where two faces meet. You can see by looking at this cube that the faces intersect in a line. That line is called an edge.
Many solid figures have more than one edge.
Vertex – a point where several planes meet in a point.
The arrow here is pointing to a vertex of this cube. Many solids have more than one vertex, we call those vertices.
Let’s look at identifying the number of faces, edges and vertices of different solids.
Here is a square pyramid.
I know this seems confusing. Think about it as if you were looking down on the pyramid. Now let’s look at the faces, edges and vertices.
The faces are the triangle sides and the square bottom. Given this, there are 5 faces in this pyramid.
The edges are where two flat surfaces meet in a line segment. Given this, there are 8 edges in this pyramid.
Faces come together at a vertex. There are five vertices in this pyramid.
Now answer the following questions about solid figures.
Example A
What do we call the points on a solid figure?
Solution: We call those vertices.
Example B
What do we call the place where two faces meet?
Solution: We call that an edge.
Example C
What are the flat sides of a figure called?
Solution: The faces
Here is the original problem once again.
Instead of quilting, Jillian and her mother went to the craft store after dinner. Jillian wanted a new box to use as a jewelry box.
"I'll get the box and then decorate it," she told her mother.
Jillian found the following box at the craft store.
"This cube is perfect," Jillian said putting into her basket.
The cube, like all solid figures is made up of different parts. Do you know what those parts are?
Every solid figure has several faces. We can count the number of faces the figure has. How many faces does each figure above have?
It has a face on the bottom and on the top. It has four faces around the sides. Therefore it has six faces in all.
The places where the faces meet is called an edge. This figure has 12 edges.
It has eight points too, and we call those points "vertices."
Vocabulary
Here are the vocabulary words in this Concept.
- Plane Figure
- a flat two-dimensional figure.
- Solid Figure
- a three-dimensional figure with height, width and depth.
- Prism
- a solid with two parallel congruent bases.
- Cylinder
- a solid with two parallel congruent circular bases.
- Pyramid
- a polygon for a base and triangular faces that meet at one vertex.
- Cone
- a solid with a circular base and one vertex
- Sphere
- a three-dimensional circular solid
- Face
- any flat surface on a solid figure
- Edge
- when two faces meet in a line segment. The line segment is the edge.
- Vertex
- when three or more faces meet at a single point.
Guided Practice
Here is one for you to try on your own.
How many edges, faces and vertices are there in this figure?
Answer
In this pyramid, there are five vertices, five faces and eight edges.
Video Review
Here is a video for review.
TenMarks: Polyhedrons - Faces, Vertices, Edges
Practice
Directions: Identify the part of each solid indicated by the arrow.
1.
2.
3.
Directions: Answer each question.
4. Define face.
5. Define edge.
6. Define vertex.
7. How many edges in a cube?
8. Which plane figures make up the faces of a square pyramid?
9. Which plane figures make up the faces of a rectangular prism?
10. How many vertices are there in a triangular pyramid?
Directions: Identify each figure.
11.
12.
13.
14.
15.
Cone
A cone is a solid three-dimensional figure with a circular base and one vertex.Cylinder
A cylinder is a solid figure with two parallel congruent circular bases.Edge
An edge is the intersection between two faces of a figure. An edge is a line segment.Face
A face is one of the flat surfaces on a solid figure.Plane Figure
A plane figure is a flat, two-dimensional figure.Prism
A prism is a three-dimensional object with two congruent parallel bases that are polygons.Pyramid
A pyramid is a three-dimensional object with a base that is a polygon and triangular faces that meet at one vertex.Solid Figure
A solid figure is a three-dimensional figure with height, width and depth.Sphere
A sphere is a round, three-dimensional solid. All points on the surface of a sphere are equidistant from the center of the sphere.Vertex
A vertex is a corner of a three-dimensional object. It is the point where three or more faces meet.Image Attributions
Description
Learning Objectives
Here you'll learn to identify the faces, edges, and vertices of solid figures.