# Math Models and Geometry

## Solve Geometry Applications: Circles and Irregular Figures

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


### Use the Properties of Circles

Do you remember the properties of circles from Decimals and Fractions Together? We’ll show them here again to refer to as we use them to solve applications.
Remember, that we approximate  with  or  depending on whether the radius of the circle is given as a decimal or a fraction. If you use the  key on your calculator to do the calculations in this section, your answers will be slightly different from the answers shown. That is because the  key uses more than two decimal places.
We usually see the formula for circumference in terms of the radius  of the circle:
But since the diameter of a circle is two times the radius, we could write the formula for the circumference in terms 
We will use this form of the circumference when we’re given the length of the diameter instead of the radius.

### Find the Area of Irregular Figures

So far, we have found area for rectangles, triangles, trapezoids, and circles. An irregular figure is a figure that is not a standard geometric shape. Its area cannot be calculated using any of the standard area formulas. But some irregular figures are made up of two or more standard geometric shapes. To find the area of one of these irregular figures, we can split it into figures whose formulas we know and then add the areas of the figures.

### Key Concepts

1. Problem Solving Strategy for Geometry Applications

2. Properties of Circles

   


### Practice Makes Perfect

Use the Properties of Circles 
In the following exercises, solve using the properties of circles.
In the following exercises, find the radius of the circle with given circumference.
Find the Area of Irregular Figures 
In the following exercises, find the area of the irregular figure. Round your answers to the nearest hundredth.
In the following exercises, solve.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.


ⓑ After looking at the checklist, do you think you are well prepared for the next section? Why or why not?
