Exercises: Solve Geometry Applications: Circles and Irregular Figures (6.3)

Exercises: Use the Properties of Circles

Instructions: For questions 1-14, solve using the properties of circles.

1. The lid of a paint bucket is a circle with radius [latex]7[/latex] inches. Find the

a. circumference and
b. area of the lid.

Solution

a. [latex]43.96[/latex] in.
b. [latex]153.86[/latex] sq. in.

2. An extra-large pizza is a circle with radius [latex]8[/latex] inches. Find the

a. circumference and
b. area of the pizza.

3. A farm sprinkler spreads water in a circle with radius of [latex]8.5[/latex] feet. Find the

a. circumference and
b. area of the watered circle.

Solution

a. [latex]53.38[/latex] ft
b. [latex]226.865[/latex] sq. ft

4. A circular rug has radius of [latex]3.5[/latex] feet. Find the

a. circumference and
b. area of the rug.

5. A reflecting pool is in the shape of a circle with diameter of [latex]20[/latex] feet. What is the circumference of the pool?
Solution

[latex]62.8[/latex] ft

6. A turntable is a circle with diameter of [latex]10[/latex] inches. What is the circumference of the turntable?
7. A circular saw has a diameter of [latex]12[/latex] inches. What is the circumference of the saw?
Solution

[latex]37.68[/latex] in.

8. A round coin has a diameter of [latex]3[/latex] centimeters. What is the circumference of the coin?
9. A barbecue grill is a circle with a diameter of [latex]2.2[/latex] feet. What is the circumference of the grill?
Solution

[latex]6.908[/latex] ft

10. The top of a pie tin is a circle with a diameter of [latex]9.5[/latex] inches. What is the circumference of the top?
11. A circle has a circumference of [latex]163.28[/latex] inches. Find the diameter.
Solution

[latex]52[/latex] in.

12. A circle has a circumference of [latex]59.66[/latex] feet. Find the diameter.

13. A circle has a circumference of [latex]17.27[/latex] meters. Find the diameter.
Solution

[latex]5.5[/latex] m

14. A circle has a circumference of [latex]80.07[/latex] centimeters. Find the diameter.

Exercises: Use the Properties of Circles

Instructions: For questions 15-18, find the radius of the circle with given circumference.
15. A circle has a circumference of [latex]150.72[/latex] feet.
Solution

[latex]24[/latex] ft

16. A circle has a circumference of [latex]251.2[/latex] centimeters.
17. A circle has a circumference of [latex]40.82[/latex] miles.
Solution

[latex]6.5[/latex] mi

18. A circle has a circumference of [latex]78.5[/latex] inches.

Exercises: Find the Area of Irregular Figures

Instructions: For questions 19-38, find the area of the irregular figure. Round your answers to the nearest hundredth.

19.

A geometric shape is shown. It is a horizontal rectangle attached to a vertical rectangle. The top is labeled 6, the height of the horizontal rectangle is labeled 2, the distance from the edge of the horizontal rectangle to the start of the vertical rectangle is 4, the base of the vertical rectangle is 2, the right side of the shape is 4.
Figure 6P.3.1
Solution

[latex]16[/latex] sq. units

20.

A geometric shape is shown. It is an L-shape. The base is labeled 10, the right side 1, the top and left side are each labeled 4.
Figure 6P.3.2

21.

A geometric shape is shown. It is a sideways U-shape. The top is labeled 6, the left side is labeled 6. An inside horizontal piece is labeled 3. Each of the vertical pieces on the right are labeled 2.
Figure 6P.3.3
Solution

[latex]30[/latex] sq. units

22.

A geometric shape is shown. It is a U-shape. The base is labeled 7. The right side is labeled 5. The two horizontal lines at the top and the vertical line on the inside are all labeled 3.
Figure 6P.3.4

23.

A geometric shape is shown. It is a rectangle with a triangle attached to the bottom left side. The top is labeled 4. The right side is labeled 10. The base is labeled 9. The vertical line from the top of the triangle to the top of the rectangle is labeled 3.
Figure 6P.3.5
Solution

[latex]57.5[/latex] sq. units

24.

A trapezoid is shown. The bases are labeled 5 and 10, the height is 5.
Figure 6P.3.6

25.

Two triangles are shown. They appear to be right triangles. The bases are labeled 3, the heights 4, and the longest sides 5.
Figure 6P.3.7
Solution

[latex]12[/latex] sq. units

26.

A geometric shape is shown. It appears to be composed of two triangles. The shared base of both triangles is 8, the heights are both labeled 6.
Figure 6P.3.8

27.

A geometric shape is shown. It is composed of two trapezoids. The base is labeled 10. The height of one trapezoid is 2. The horizontal and vertical sides are all labeled 5.
Figure 6P.3.9
Solution

[latex]67.5[/latex] sq. units

28.

A geometric shape is shown. It is a trapezoid attached to a triangle. The base of the triangle is labeled 6, the height is labeled 5. The height of the trapezoid is 6, one base is 3.
Figure 6P.3.10

29.

A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 8, the bottom is 8, the right side is 13, and the width of the smaller rectangle is 2.
Figure 6P.3.11
Solution

[latex]89[/latex] sq. units

30.

A geometric shape is shown. It is a rectangle with a triangle and another rectangle attached. The left side is labeled 12, the right side 7, the base 6. The width of the smaller rectangle is labeled 1.
Figure 6P.3.12

31.

A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.
Figure 6P.3.13
Solution

[latex]44.81[/latex] sq. units

32.

A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 10, the height is 6. The portion of the rectangle on the left of the semi-circle is labeled 5, the portion on the right is labeled 2.
Figure 6P.3.14

33.

A geometric shape is shown. A triangle is attached to a semi-circle. The base of the triangle is labeled 4. The height of the triangle and the diameter of the circle are 8.
Figure 6P.3.15
Solution

[latex]41.12[/latex] sq. units

34.

A geometric shape is shown. A triangle is attached to a semi-circle. The height of the triangle is labeled 4. The base of the triangle, also the diameter of the semi-circle, is labeled 4.
Figure 6P.3.16

35.

A geometric shape is shown. It is a rectangle attached to a semi-circle. The base of the rectangle is labeled 5, the height is 7.
Figure 6P.3.17
Solution

[latex]35.13[/latex] sq. units

36.

A geometric shape is shown. A trapezoid is shown with a semi-circle attached to the top. The diameter of the circle, which is also the top of the trapezoid, is labeled 8. The height of the trapezoid is 6. The bottom of the trapezoid is 13.
Figure 6P.3.18

37.

A geometric shape is shown. It is a rectangle with a triangle attached to the top on the left side and a circle attached to the top right corner. The diameter of the circle is labeled 5. The height of the triangle is labeled 5, the base is labeled 4. The height of the rectangle is labeled 6, the base 11.
Figure 6P.3.19
Solution

[latex]95.625[/latex] sq. units

38.

A geometric shape is shown. It is a trapezoid with a triangle attached to the top, and a circle attached to the triangle. The diameter of the circle is 4. The height of the triangle is 5, the base of the triangle, which is also the top of the trapezoid, is 6. The bottom of the trapezoid is 9. The height of the trapezoid is 7.
Figure 6P.3.20

Exercises: Find the Area of Irregular Figures

Instructions: For questions 39-42, solve.
39. A city park covers one block plus parts of four more blocks, as shown. The block is a square with sides [latex]250[/latex] feet long, and the triangles are isosceles right triangles. Find the area of the park.

A square is shown with four triangles coming off each side.
Figure 6P.3.21
Solution

[latex]187\text{,}500[/latex] sq. ft

40. A gift box will be made from a rectangular piece of cardboard measuring [latex]12[/latex] inches by [latex]20[/latex] inches, with squares cut out of the corners of the sides, as shown. The sides of the squares are [latex]3[/latex] inches. Find the area of the cardboard after the corners are cut out.
A rectangle is shown. Each corner has a gray shaded square. There are dotted lines drawn across the side of each square attached to the next square.
Figure 6P.3.22
41. Perry needs to put in a new lawn. His lot is a rectangle with a length of [latex]120[/latex] feet and a width of [latex]100[/latex] feet. The house is rectangular and measures [latex]50[/latex] feet by [latex]40[/latex] feet. His driveway is rectangular and measures [latex]20[/latex] feet by [latex]30[/latex] feet, as shown. Find the area of Perry’s lawn.

A rectangular lot is shown. In it is a home shaped like a rectangle attached to a rectangular driveway.
Figure 6P.3.23
Solution

[latex]9400[/latex] sq. ft

42. Denise is planning to put a deck in her back yard. The deck will be a [latex]\text{20-ft}[/latex] by [latex]\text{12-ft}[/latex] rectangle with a semicircle of diameter [latex]6[/latex] feet, as shown below. Find the area of the deck.

A picture of a deck is shown. It is shaped like a rectangle with a semi-circle attached to the top on the left side.
Figure 6P.3.24

Exercises: Everyday Math

Instructions: For questions 43-44, answer the given everyday math word problems.

43. Area of a Tabletop Yuki bought a drop-leaf kitchen table. The rectangular part of the table is a [latex]\text{1-ft}[/latex] by [latex]\text{3-ft}[/latex] rectangle with a semicircle at each end, as shown.

a. Find the area of the table with one leaf up.
b. Find the area of the table with both leaves up.

 

An image of a table is shown. There is a rectangular portion attached to a semi-circular portion. There is another semi-circular leaf folded down on the other side of the rectangle.
Figure 6P.3.25
Solution

a. [latex]6.5325[/latex] sq. ft
b. [latex]10.065[/latex] sq. ft

44. Painting Leora wants to paint the nursery in her house. The nursery is an [latex]\text{8-ft}[/latex] by [latex]\text{10-ft}[/latex] rectangle, and the ceiling is [latex]8[/latex] feet tall. There is a [latex]\text{3-ft}[/latex] by [latex]\text{6.5-ft}[/latex] door on one wall, a [latex]\text{3-ft}[/latex] by [latex]\text{6.5-ft}[/latex] closet door on another wall, and one [latex]\text{4-ft}[/latex] by [latex]\text{3.5-ft}[/latex] window on the third wall. The fourth wall has no doors or windows. If she will only paint the four walls, and not the ceiling or doors, how many square feet will she need to paint?

Exercises: Writing Exercises

Instructions: For questions 45-46, answer the given writing exercises.

45. Describe two different ways to find the area of this figure, and then show your work to make sure both ways give the same area.

A geometric shape is shown. It is a vertical rectangle attached to a horizontal rectangle. The width of the vertical rectangle is 3, the left side is labeled 6, the bottom is labeled 9, and the width of the horizontal rectangle is labeled 3. The top of the horizontal rectangle is labeled 6, and the distance from the top of that rectangle to the top of the other rectangle is labeled 3.
Figure 6P.3.26
Solution

Answers will vary.

46. A circle has a diameter of [latex]14[/latex] feet. Find the area of the circle

a. using [latex]3.14[/latex] for[latex]\pi[/latex]
b. using [latex]\frac{22}{7}[/latex] for [latex]\text{π}.[/latex]
c. Which calculation to do prefer? Why?

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Fanshawe Pre-Health Sciences Mathematics 1 Copyright © 2022 by Domenic Spilotro, MSc is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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