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

- Computer Science 336: Network Forensics
- Computer Science 220: Fundamentals of Routing and Switching
- Global Competency Fundamentals & Applications
- Introduction to the Principles of Project Management
- Praxis Elementary Education: Reading & Language Arts - Applied CKT (7902): Study Guide & Practice
- Practical Applications for Business Ethics
- Practical Applications for Marketing
- Practical Applications for HR Management
- Practical Applications for Organizational Behavior
- Analyzing Texts Using Writing Structures
- MBLEx Prep Product Comparison
- AEPA Prep Product Comparison
- ASCP Prep Product Comparison
- NCE Prep Product Comparison
- TASC Test Score Information
- What is the TASC Test?
- Praxis Prep Product Comparison

- Diclofenac vs. Ibuprofen
- Developing & Managing a High-Quality Library Collection
- Library Space Planning
- Literacy Strategies for Teachers
- Arithmetic Operations in R Programming
- Practical Application: Understanding Employee Behavior
- Positive Global Outcomes of Global Competence
- Practical Application: Color Wheel Infographic
- Quiz & Worksheet - Developing a Learner-Centered Classroom
- Quiz & Worksheet - Technology for Teaching Reading
- Quiz & Worksheet - Pectoralis Major Anatomy
- Quiz & Worksheet - Oral & Written Communication Skills
- Quiz & Worksheet - How to Teach Reading to ELL Students
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- High School Trigonometry: Homework Help Resource
- NY Regents Exam - Chemistry: Help and Review
- Contemporary Math Remediation
- Middle School Physical Science: Homeschool Curriculum
- DSST Health & Human Development: Study Guide & Test Prep
- Using Your Athletic Scholarship
- Psychological Consultation & Collaboration in School Settings
- Quiz & Worksheet - Response Variable in Statistics
- Quiz & Worksheet - Flynn Effect
- Quiz & Worksheet - Teaching Teachers How to Teach
- Quiz & Worksheet - Methods for Scaffolding in Education
- Quiz & Worksheet - Observational Learning Theory

- How to Differentiate Math Instruction
- Practical Application: Steps in the Communication Process Infographic
- Crusades Lesson Plan
- Earth Day Project Ideas
- California Science Standards
- NYS Regents Exam Schedule
- Community Lesson Plan
- Plate Tectonics Activities for Kids
- Circulatory System Experiments for Kids
- GMAT Registration Information
- Homeschooling in Illinois
- Best LSAT Prep Course

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

Browse by subject