9.5 Solve Geometry Applications: Circles and Irregular Figures

Learning Objectives

By the end of this section, you will be able to:

  • Use the properties of circles
  • Find the area of 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

Step 1. Read the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.

Step 2. Identify what you are looking for.

Step 3. Name what you are looking for. Choose a variable to represent that quantity.

Step 4. Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.

Step 5. Solve the equation using good algebra techniques.

Step 6. Check the answer in the problem and make sure it makes sense.

Step 7. Answer the question with a complete sentence.

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 π with 3.14 or 227 depending on whether the radius of the circle is given as a decimal or a fraction. If you use the π 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 π key uses more than two decimal places.

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.

Media

ACCESS ADDITIONAL ONLINE RESOURCES

  • Circumference of a Circle
  • Area of a Circle
  • Area of an L-shaped polygon
  • Area of an L-shaped polygon with Decimals
  • Perimeter Involving a Rectangle and Circle
  • Area Involving a Rectangle and Circle

Section 9.5 Exercises

Practice Makes Perfect

Use the Properties of Circles

In the following exercises, solve using the properties of circles.
217.The lid of a paint bucket is a circle with radius 7 inches. Find the ⓐ circumference and ⓑ area of the lid.
218.An extra-large pizza is a circle with radius 8 inches. Find the ⓐ circumference and ⓑ area of the pizza.
219.A farm sprinkler spreads water in a circle with radius of 8.5 feet. Find the ⓐ circumference and ⓑ area of the watered circle.
220.A circular rug has radius of 3.5 feet. Find the ⓐ circumference and ⓑ area of the rug.
221.A reflecting pool is in the shape of a circle with diameter of 20 feet. What is the circumference of the pool?
222.A turntable is a circle with diameter of 10 inches. What is the circumference of the turntable?
223.A circular saw has a diameter of 12 inches. What is the circumference of the saw?
224.A round coin has a diameter of 3 centimeters. What is the circumference of the coin?
225.A barbecue grill is a circle with a diameter of 2.2 feet. What is the circumference of the grill?
226.The top of a pie tin is a circle with a diameter of 9.5 inches. What is the circumference of the top?
227.A circle has a circumference of 163.28 inches. Find the diameter.
228.A circle has a circumference of 59.66 feet. Find the diameter.
229.A circle has a circumference of 17.27 meters. Find the diameter.
230.A circle has a circumference of 80.07 centimeters. Find the diameter.

In the following exercises, find the radius of the circle with given circumference.
231.A circle has a circumference of 150.72 feet.
232.A circle has a circumference of 251.2 centimeters.
233.A circle has a circumference of 40.82 miles.
234.A circle has a circumference of 78.5 inches.

Self Check

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

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