# Ch 18: Perimeter, Area & Volume in Geometry

### About This Chapter

## Perimeter, Area & Volume in Geometry - Chapter Summary

Take advantage of video lessons covering perimeter, area and volume to prepare for the multiple-choice questions and word problems included on the math portion of the CAHSEE. This chapter is designed to teach you formulas for calculating:

- Circumference and area of circles
- Area and perimeter of triangles and rectangles
- Volume of cylinders, cones, spheres, prisms and pyramids
- Area of complex and irregular two-dimensional figures
- Perimeter and area of rectangular and irregular three-dimensional figures

Use this chapter's short, engaging video lessons and transcripts to familiarize yourself with the dimensions and mathematical functions needed to solve these types of problems. You can even get an idea of how actual test questions are formatted with the self-assessment quizzes included at the end of each lesson. This resource includes links back to corresponding video content and practice problems.

### Perimeter, Area & Volume in Geometry - Objectives

If you're a high school student in California, passing scores on the CAHSEE's math portion are among the requirements for a diploma. The test is administered to sophomores and includes 80 multiple-choice questions. Video lessons and quizzes included in this chapter are designed to help you prepare for the 17 questions found in the Measurement and Geometry section.

On this part of the exam, you'll be given a series of two- or three-dimensional shapes and asked to select an answer representing the correct area, surface area, perimeter, circumference or volume. A word problem requiring you to combine these geometry skills is included at the end of the section.

### 1. Overview of Three-dimensional Shapes in Geometry

We are surrounded by three-dimensional shapes. Watch this video lesson to see what some three-dimensional shapes look like, such as a cube, a sphere, a brick, and a cylinder.

### 2. Perimeter of Triangles and Rectangles

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

### 3. Area of Triangles and Rectangles

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

### 4. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

### 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.

### 6. Volume of Prisms and Pyramids

In this lesson, we'll learn about prisms and pyramids. We'll look at the different types of prisms and pyramids, as well as practice calculating volume for each shape.

### 7. How to Find Surface Area of a Cube and a Rectangular Prism

After watching this video lesson, you will be able to use the formula for the surface area of a rectangular prism. You will know what measurements you need to use it and how you can apply it to a cube as well.

### 8. How to Find Surface Area of a Cylinder

Watch this video lesson to learn the formula you can use to find the surface area of a cylinder. Learn the measurements that you'll need as well as how to use them.

### 9. How to Find Surface Area of a Pyramid

In this video lesson, we will learn how to take any pyramid, whether it's a pyramid in Egypt or a little toy pyramid, and calculate how much paint we will need to paint it. Learn the formula and what is behind it.

### 10. Area of Complex & Irregular 2D & 3D Shapes

This lesson will help you find the area of any 2D or 3D shape. From houses to the craziest images of your dreams, you'll be able to use basic geometry to find the area of just about anything.

### 11. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures

How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.

### 12. Area: Real-World Geometry Problems

View this lesson to see how you can use geometric area in real-world situations, like mowing the lawn or picking out which carpet installer you should hire. A quick area review and quiz are also included.

### 13. Perimeter: Real-World Geometry Problems

Watch this lesson to get some practice using perimeter in real-world situations. If you like baking brownies, you'll be able to use the math here to make your creations even more delicious!

### 14. Volume: Real-World Geometry Problems

Volume isn't just a concept you use in textbooks! It's all around you in the real world. In this lesson, you'll work through two examples of real-world geometry problems and then get some more practice with a quiz.

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### Other Chapters

Other chapters within the CAHSEE Math Exam: Test Prep & Study Guide course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Algebraic Linear Equations & Inequalities
- Problems with Exponents
- Overview of Functions
- Rational Expressions & Practice
- Calculations with Ratios, Percent & Proportions
- Understanding Matrices & Absolute Value
- Quadratics & Polynomials
- Geometry: Graphing Basics
- Graphing on the Coordinate Plane
- Measurement in Math
- Properties of Shapes
- Triangles, the Pythagorean Theorem & Congruency
- Statistics, Probability & Working with Data
- Mathematical Reasoning
- Basic Mathematical Logic
- CAHSEE Math Exam Flashcards