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Ch 7: Geometric Expressions, Equations & Relationships

About This Chapter

The text and video lessons in this chapter are on the subject of geometric expressions, equations and relationships. We present information on the Pythagorean Theorem, definitions and formulas for surface areas, and more.

Geometric Expressions, Equations & Relationships - Chapter Summary

Let our subject-matter experts help you show your students about geometric expressions, equations and relationships. These lessons will present your students with an explanation of the Pythagorean Theorem using models and diagrams, the definition of surface area, and additional lesson topics, like:

  • The Pythagorean Theorem
  • Determining the area of cylinders
  • Volume of spheres, cylinders and cones
  • Surface area formulas
  • Definition and formulas for lateral and total surface areas

Lessons are short, with video run times between 5-10 minutes. We provide a feature that allows your students submit questions directly to a Study.com expert.

8 Lessons in Chapter 7: Geometric Expressions, Equations & Relationships
Test your knowledge with a 30-question chapter practice test
Pythagorean Theorem: Definition & Example

1. Pythagorean Theorem: Definition & Example

Learn what the Pythagorean Theorem says about a right triangle and the relationships of its three sides to each other by watching this video lesson. Also learn how you can use this to your advantage when solving problems.

Explaining the Pythagorean Theorem with Models & Diagrams

2. Explaining the Pythagorean Theorem with Models & Diagrams

It's one of the most important math formulas they'll ever learn, yet many students can't effectively use the Pythagorean Theorem. This lesson will discuss and demonstrate how to use diagrams and models to explain the Pythagorean theorem.

The Pythagorean Theorem: Converse and Special Cases

3. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

What Are Cylinders? - Definition, Area & Volume

4. What Are Cylinders? - Definition, Area & Volume

Watch this video lesson to learn why soda cans are cylinders and the method by which you can discover how much soda can fit inside by finding the volume. You will also learn about finding a cylinder's surface area.

Volume of Cylinders, Cones, and Spheres

5. Volume of Cylinders, Cones, and Spheres

In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.

What is Surface Area? - Definition & Formulas

6. What is Surface Area? - Definition & Formulas

In this lesson, you use general and specific formulas to learn how to find the surface area of three-dimensional shapes, such as cubes, prisms, spheres, cones and cylinders.

Lateral Surface Area: Definition & Formula

7. Lateral Surface Area: Definition & Formula

In this lesson, you will learn the definition of the lateral surface area of a three-dimensional object. You will apply lateral surface area formulas for some three-dimensional shapes to see how to find the lateral surface area of various objects.

Total Surface Area: Definition & Formula

8. Total Surface Area: Definition & Formula

This lesson will define and explain what total surface area is and provide the formulas for calculating total surface area, as well as an explanation about why they work.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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