Geometric Solids and Surface Area

Contributor: Erika Wargo. Lesson ID: 12577

You probably don't care about the surface area of your tissue box, as long as you can get a tissue and blow your nose! Someone had to design the box that holds the tissues. That requires surface area!

categories

Geometry, Solid Geometry (3D)

subject
Math
learning style
Auditory, Kinesthetic, Visual
personality style
Beaver
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

three geometric solids

The three items shown above are quite different; however, they all have one thing in common — they are three-dimensional geometric shapes.

  • What 3D geometric shapes are represented by the objects above?
  • What other geometric shapes can you name as you look around?

Read on to find out how your knowledge in the area of geometry shapes up!

Shapes that take up space are called geometric solids.

Geometric solids are real-world objects that you see every day. They are three-dimensional, like houses, people, toys, and books.

The word "solid" in a geometric solid does not mean that the object has to be filled. It can be hollow, like an empty cube-shaped box.

In math, the word "solid" means that it is 3-dimensional, takes up space, and has a height, length, and width that you can measure.

Before you watch two videos to introduce you to geometric solids, create a table similar to the table below or print the Geometric Solids found in the Downloadable Resources in the right-hand sidebar.

Fill in your table with what you already know about geometric solids. In the top section, see if you can define the geometric terms. In the bottom section, write down features of each geometric solid (optional: include a quick sketch).

Three-dimensional shapes can be created by using two-dimensional shapes, such as circles, triangles, squares, or rectangles. Two-dimensional shapes are flat, but three-dimensional shapes have depth.


Now that you are familiar with geometric shapes, learn more about the parts that make up the shapes. Complete the following steps:

  1. Go to Edges, Faces, Vertices (Scholastic, Inc.) and click on the STEP BY STEP button to watch how to identify the edges, faces, and vertices of geometric solids. Click on the NEXT and SHOW ME buttons to progress through the steps.
  2. Click on WATCH OUT! to learn more about three-dimensional figures.
  3. Go back to the main page and click on the STEP BY STEP button. Click on TRY IT! to practice identifying features of three-dimensional shapes.
  4. Return to the main page and click on the Test Yourself button and answer the questions. If you did not score 4 or more correct, you may want to go back to the Get It! section and review the lesson.

In your math journal, write a response to the following:

  1. In your own words, explain at least two facts about geometric solids.
  2. How are 3D shapes different from 2D shapes?

The total area of a three-dimensional object is called surface area. The surface area is found by adding the area of each face together. If a figure has six faces, you will find the area of each face and add them together. You can use the following formulas to calculate the surface area of a rectangular solid:

total surface area = area of top + area of bottom + area of front + area of back + area of side + area of side

surface area = 2lw + 2lh + 2wh, where l=length, w=width, h=height

Learn about how to find the surface area of the geometric shapes you have learned about by completing the following steps:

  1. Go to Surface Area (Scholastic, Inc.) and click on the STEP BY STEP button to watch how to calculate the surface area of ageometric solid. Click on the NEXT and SHOW ME buttons to progress through the steps.
  2. Click on WATCH OUT! to learn about finding the surface area of a cube.
  3. Click on TRY IT! to practice finding the surface area of a cube and rectangular prism.

In your math journal, write a response to the following:

  1. Explain how finding the area of a 2D shape is similar to and different from finding the area of a 3D shape.
  2. Explain a time when finding the surface area would be helpful in real life.

In the Got It? section, you will practice identifying features of geometric solids and calculating the surface area with interactive games and practice.

Elephango's Philosophy

We help prepare learners for a future that cannot yet be defined. They must be ready for change, willing to learn and able to think critically. Elephango is designed to create lifelong learners who are ready for that rapidly changing future.