# Ch 7: Solving Basic Geometric Problems

### About This Chapter

## Solving Basic Geometric Problems - Chapter Summary

This chapter covers solving basic geometric problems for your review. When you work through these lessons, you'll study the formulas for diameter and perimeter, the definition of area, and the properties of similar and congruent shapes. Once you complete this chapter, you should be able to:

- Describe how dimension changes affect perimeter, area, surface area and volume
- Use a formula to determine the radius of a circle
- Differentiate between area and circumference in a circle
- Define surface area and the volume of shapes
- Discuss 2D views of 3D objects
- Explain the properties of similar and congruent solids
- Apply scale factors to the area, volume and perimeter of similar figures

It's easy to get ready for an exam or complete your homework with help from these mobile-friendly lessons and quizzes, which you can access 24 hours a day on your mobile phone, tablet or computer. Our lessons are short and accompanied by multiple-choice quizzes you can use to test your understanding. If you have any questions about these topics, use the Dashboard to submit them for one of our expert instructors to answer.

### 1. What is Perimeter? - Definition & Formula

In mathematics, the perimeter is the distance around a two-dimensional shape. The formula for finding the perimeter of certain shapes will be discussed in this lesson, and there will be some examples to help you understand how to calculate the perimeter.

### 2. What is Area in Math? - Definition & Formula

Area is the size of a two-dimensional surface. This lesson will define area, give some of the most common formulas, and give examples of those formulas. A quiz at the end of the lesson will allow you to work out some area problems on your own.

### 3. How Changes in Dimensions Affect Area & Perimeter

Tweaking just one dimension in a figure can make an important difference in its perimeter and area. In this lesson, we'll look at rectangles, pentagons, and circles to explore how a change in one dimension can affect a figure's area and perimeter.

### 4. Properties of Congruent and Similar Shapes

In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.

### 5. What is Diameter? - Definition & Formula

In this lesson, you can find out how important the diameter is to a circle. Also, you can learn about the formulas that were figured out by the mathematicians of old relating to the diameter and how to use them.

### 6. How to Find the Radius of a Circle: Definition & Formula

In this lesson, you will discover the definition of a radius. You will also learn how to find the radius of a circle using three different formulas based on diameter, circumference, and area.

### 7. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. In this lesson, learn how to find the area and circumference of circles by working through several examples.

### 8. 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.

### 9. Volumes of Shapes: Definition & Examples

Volume is defined as the 3-dimensional space enclosed by a boundary. In this lesson we will define volume, give some of the most common formulas and then work some example problems to become familiar with the formulas. There will be a quiz at the end of the lesson for practice.

### 10. How Changes in Dimension Affect Surface Area & Volume

What happens to the surface area and volume of a shape like a sphere when the dimensions of the shape change? In this lesson, learn how change in the dimensions of common shapes like spheres and cylinders affect surface area and volume.

### 11. Properties of Congruent & Similar Solids

Watch this video lesson and you will learn the one characteristic that all congruent solids have and you will learn how the volumes of similar solids are related to their similarity ratio.

### 12. 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.

### Earning College Credit

Did you know… We have over 220 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

### Transferring credit to the school of your choice

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.

### Other Chapters

Other chapters within the GACE Special Education Mathematics & Science (088): Practice & Study Guide course

- Working with Real Numbers
- Fractions, Decimals, Percents & Ratios
- Understanding Number Theory & Estimation
- Overview of Basic Algebra
- Patterns & Sequences in Algebra
- Characteristics & Relationships of Functions
- Points, Lines, Rays & Angles
- Solving Angle Problems with Triangles & Quadrilaterals
- Geometric Relationships in the Coordinate Plane
- Solving Problems Involving Systems of Measurement
- Displaying & Interpreting Data
- Measures of Central Tendency
- Statistical Models & Processes
- Understanding Probability, Combinations & Permutations
- Scientific Inquiry & Design
- Nature of Scientific Knowledge
- Major Developments & Historical Figures in Science
- Collecting & Evaluating Scientific Data
- Science Laboratory & Field Equipment Safety
- Environmental Effects of Science & Technology
- Energy Production & Natural Resource Management
- Science & Technology in Consumer Products
- Atoms, Energy & Matter
- Concepts & Relationships Between Energy & Matter
- Basics of the Periodic Table
- Chemical Compounds & Reactions
- Acid-Base Chemistry
- Solutions & Solubility
- Concepts of Mechanics Overview
- Electricity & Magnetism Overview
- Waves & Optics Overview
- Structure & Function of Cells & Organelles
- Basic Biochemistry of Life
- Basic Genetics
- Evolution, Natural Selection & Biological Diversity
- Hierarchical Classification of Living Things
- Understanding Plant Structures & Function
- Animal & Human Anatomy & Physiology
- Population Dynamics & Ecology
- Rocks, Minerals & Soil Overview
- Earth's Structure, Shape & Processes
- Historical Geology
- Understanding the Earth's Oceans
- Freshwater Characteristics & Processes
- Atmosphere & Weather
- Climate, Seasons & Geography
- Exploring Features of the Solar System
- Earth-Moon-Sun System
- GACE Special Education Mathematics & Science Flashcards