Back To Course

High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Karin Gonzalez*

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, you will learn the definition of a triangular pyramid. You will also learn the formulas to find the base area, surface area, and volume of a triangular pyramid. Then work through an example calculation of each.

The first thing that comes to mind when thinking of pyramids may be the Great Pyramids of Egypt. If you look at a picture of these historical pyramids, you can see that their base is actually a square. Therefore, they are considered square pyramids, not triangular pyramids.

So what is a **pyramid**? It is a polyhedron or three-dimensional shape with at least three sides and polygonal base. A **triangular pyramid** is a pyramid with a triangle as a base and three triangular faces. It has four vertices or points and six edges.

There are also rectangular, pentagonal, square, and hexagonal pyramids. Can you guess what these are? Yes! They are pyramids with rectangular, pentagonal, square, and hexagonal bases, respectively.

There are three main components of a triangular pyramid. First is the base, which is a triangle, of course. Next are the faces, which are three triangles. Last is the **apex**, which is the point at the top where all of the faces meet. Easy enough! There are some important measurements as well: height, base length, apothem length, and the slant height. Whoa! What are apothem length and slant height, you may say? Here is a diagram to illustrate these parts of a triangular pyramid:

The slant height, base length, and apothem length are indicated in blue.

Height is the perpendicular line going from the point of the triangle to the midpoint of the base.

There are three main formulas for a triangular pyramid. First is the formula to find the base area of the triangular pyramid:

The **surface area** is the area of the outer layer or outer surfaces of a structure. So, the surface area of a triangular pyramid is the area of the surfaces of the three triangle faces and the triangular base. Because each surface is a triangle, to find area is basically multiplying the base times height and dividing it by two.

The formula is this:

In order to find the volume for a triangular pyramid, the area of the base and the height of the triangular pyramid must be know. Once these measurements are calculated, find the volume of a triangular pyramid with this formula:

Find the base area, surface area, and volume of a triangular pyramid with the following measurements:

Apothem Length = 8 cm

Base Length = 14 cm

Height = 20 cm

Slant Height = 22 cm

To find the base area of the triangular pyramid, plug the given values into the formula:

To find the surface area of the triangular pyramid, plug the given values into the formula:

To find the volume of the triangular pyramid, plug in the area that was already calculated into the formula:

**Pyramids** are polyhedrons with a polygonal base and triangular sides that meet at the apex. A** triangular pyramid** is a pyramid with a triangle base and three triangular faces, four vertices, and six edges. Base area, surface area, and the volume of a triangular pyramid can be calculated using the dimensions of the pyramid and the given formulas:

Base Area = (Apothem Length * Base Length) / 2

Surface Area = (Apothem Length * Base Length) / 2 + (3 * Base Length * Slant Height) / 2

Volume = (Base Area * Height) / 3

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
10 in chapter 22 of the course:

Back To Course

High School Trigonometry: Homework Help Resource30 chapters | 203 lessons

- Trigonometric Ratios and Similarity 6:49
- Practice Finding the Trigonometric Ratios 6:57
- The Pythagorean Theorem: Practice and Application 7:33
- Finding Distance with the Pythagorean Theorem 6:54
- Trigonometry and the Pythagorean Theorem 4:14
- Perfect Square: Definition, Formula & Examples 2:55
- Solid Figures: Definition, Properties & Examples 4:20
- Sphere: Definition & Formulas 4:56
- Trigonal Bipyramidal in Molecular Geometry: Bond Angles & Shape
- What is a Triangle Pyramid? - Definition & Formula 4:56
- Go to Triangle Trigonometry: Homework Help

- Introduction to SQL
- Computer Science 203: Defensive Security
- GRE Information Guide
- Computer Science 310: Current Trends in Computer Science & IT
- Earth Science 105: Introduction to Oceanography
- Views, Indexes & Triggers in SQL
- Joins & Subqueries in SQL
- Intro to Databases & SQL
- SQL Data Types & Syntax
- Removing Data Using SQL
- What is the ASCP Exam?
- ASCPI vs ASCP
- MEGA Exam Registration Information
- MEGA & MoGEA Prep Product Comparison
- PERT Prep Product Comparison
- MTLE Prep Product Comparison
- What is the MTLE Test?

- Separation Methods Used in Biology Labs
- Job Enrichment: Definition, Advantages, Disadvantages & Examples
- Measurement Lesson for Kids
- How Plants Grow: Lesson for Kids
- How a Bill Becomes a Law Lesson Plan
- Computer Technology Lesson Plan
- Responsibility-Based A/R Reporting in Health: Definition & Purpose
- Quiz & Worksheet - Southern Early Childhood Association
- Quiz & Worksheet - Bleak House
- Quiz & Worksheet - Psychological Impact of Social Media
- Quiz & Worksheet - Intonation & Stress in Speaking
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Middle School Math Worksheets
- Differentiated Instruction in Classrooms

- PLACE Mathematics: Practice & Study Guide
- Prentice Hall Chemistry: Online Textbook Help
- College Mathematics Remediation
- Benefits of Customer Relationship Management (CRM)
- GACE School Psychology (605): Practice & Study Guide
- SPHRi Certification: Employee Relations & Communication
- TExES Science 7-12: Acid-Base Chemistry
- Quiz & Worksheet - Population Distribution Factors
- Quiz & Worksheet - Characteristics of Series Circuits
- Quiz & Worksheet - Creating a Business Pitch
- Quiz & Worksheet - Writing a Customer Service Email
- Quiz & Worksheet - Dividing Decimals Steps & Rules

- Venus, Roman Goddess of Love: Importance & Mythology
- The Plague of Justinian
- Orange County Adult Education
- To Be, Or Not To Be: Quote Analysis
- Online Credit Recovery Programs
- Manifest Destiny Lesson Plan
- Can You Use a Calculator on the GMAT?
- Political Spectrum Lesson Plan
- Getting Started with Study.com's College Courses: Student Tour
- Collage Lesson Plan
- How to Create Assignments in Your Study.com Virtual Classroom
- How to Use Study.com to Boost Your Employees' Skills

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject