Introduction to Solving Problems With Circles and Irregular Figures

What you’ll learn to do: Use the properties of circles and irregular figures to solve problems

A birthday cake with candles and the words "happy birthday" written on it.

It is your coworkers birthday tomorrow and you decide to make a cake to bring to the office. The container you have is a square with side length 12 inches exactly. If your cake will be circular, what is the largest cake you can make? To find out, you will need to understand the properties of circles. In this chapter, you will also learn about the areas of irregular figures.

Before you get started, take this readiness quiz.

Readiness Quiz


If you missed this problem, review this example.

Evaluate [latex]{x}^{2}[/latex] when [latex]x=10[/latex].




If you missed either of these problems, review these videos.


In this section, we’ll continue working with geometry applications. We will add several new formulas to our collection of formulas. To help you as you do the examples and exercises in this section, we will show the Problem Solving Strategy for Geometry Applications here.

Problem Solving Strategy for Geometry Applications

Read the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.
Identify what you are looking for.
Name what you are looking for. Choose a variable to represent that quantity.
Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
Solve the equation using good algebra techniques.
Check the answer in the problem and make sure it makes sense.
Answer the question with a complete sentence.