Practice For use with pages

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1 11.1 For use with pages Find the area of the polygon The lengths of the hypotenuse and one leg of a right triangle are given. Find the perimeter and area of the triangle. 7. Hypotenuse: 26 cm; leg: 24 cm. Hypotenuse: 50 mm; leg: 14 mm 9. Hypotenuse: 37 ft; leg: 12 ft 10. Hypotenuse: 5 in.; leg: 77 in. Find the value of x ft cm in ft x ft 33 cm x cm 21 in. x in. Find the area of the shaded polygon m ft 6 m 16 ft 7 ft 10 m cm 12 in. 14 cm 11 in. 22 in. in. 26 cm mm mm ft 3 mm 24 ft 32 ft 1 ft Chapter 11 Resource Book 143

2 11.1 continued For use with pages Graph the points and connect them to form a polygon. Find the area of the polygon. 20. (2, 2), B(3, 6), C(5, 6), D(4, 2) 21. P(24, 24), Q(21, 21), R(5, 24) y y 2 2 x 1 1 x Find the height and area of the polygon in in m 17 m Envelopes You have an envelope that is 9.5 inches by 4.2 inches and has a triangular flap with a height of 2.4 inches. What is the area of the envelope shown in the diagram? 2.4 in. 4.2 in. 9.5 in. 25. Floor Tile You have a piece of floor tile in the shape of a parallelogram that has a base of 6 feet and a height of 2.5 feet. You cut a triangular piece of tile with a base of 2 feet to fit next to the other piece, as shown. Find the total area of the tile in square feet and square inches. 26. Painting painter is painting the back of your garage, which has the measurements shown. The painter can paint 200 square feet per hour and charges $25 per hour. How much will you have to pay if the painter rounds the time spent painting to the nearest half hour? 24 ft 45 6 ft 2 ft 2.5 ft 32 ft 144 Chapter 11 Resource Book

3 11.2 For use with pages Find the area of the trapezoid Find the area of the rhombus or kite Use the given information to find the value of x. 10. rea in rea ft rea 5 17 cm 2 x in. x ft 15 in. Find the area of the figure. 21 ft 17 cm x cm 2 ft 13. y 14. y 15. y x 1 3 x 1 6 cm x Chapter 11 Resource Book 145

4 11.2 continued For use with pages Find the area of the polygon Washing Windows You are going to wash a large 10 ft glass window in the shape of a trapezoid. The lengths of the bases of the window are 10 feet and 14 feet. The height is feet. You can wash 6 square feet of ft the window in 1 minute. How long will it take you to wash the entire window? 23. Company Logo company has a logo that is in the shape of a rhombus. The company wants to put its logo on a sign outside the building. On the sign, the diagonals of the rhombus will be 72 and 36 inches long. Find the area of the logo. 14 ft 72 in. 24. Flower Decoration You are making a flower decoration for your house in the shape of a kite. The area of the decoration is 450 square centimeters and the length of one diagonal is 25 centimeters. Find the length of the other diagonal. 36 in. 146 Chapter 11 Resource Book

5 11.3 For use with pages Complete the table of ratios for similar polygons. Ratio of corresponding side lengths Ratio of perimeters Ratio of areas 1. 5 : 2. 4 : : : 1 5? Corresponding lengths in similar figures are given. Find the ratios (shaded to unshaded) of the perimeters and areas. Find the unknown area ft 2 2 ft 5 ft in in. 20 in cm mm 2 22 cm 1 cm 24 mm 9 mm The ratio of the areas of two similar figures is given. Write the ratio of the lengths of corresponding sides. 9. Ratio of areas 5 16 : Ratio of areas 5 25 : Ratio of areas : 49 Use the given area to find XY. 12. BCD, WXYZ 13. EFGHJK, UVWXYZ B 15 in. C X Y W Z D in in. 2 F G E H cm U X K J Z Y 5 16 cm cm 2 V W Chapter 11 Resource Book 147

6 11.3 continued For use with pages Regular octagon BCDEFGH has a side length of 10 millimeters and an area of 160 square millimeters. Regular octagon JKLMNOPQ has a perimeter of 200 millimeters. Find its area. 15. Kites RSTU and VWXY are similar. The area of RSTU is 162 square feet. The diagonals of VWXY are 32 feet long and 1 feet long. Find the area of VWXY. Then use the ratio of the areas to find the lengths of the diagonals of RSTU. 16. n BC and n DEF are similar. The height of n BC is 42 inches. The base of n DEF is 7 inches and the area is 42 square inches. Find the ratio of the area of n BC to the area of n DEF. 17. Rectangles BCD and EFGH are similar. The width of BCD is 1 centimeters and the perimeter is 120 centimeters. The length of EFGH is 91 centimeters. Find the ratio of the side lengths of BCD to the side lengths of EFGH. 1. Posters Your school had a car wash to raise money. poster that was used to attract customers is shown. You decide that you will have the car wash again next year. You will have a similar poster but you will increase the length to 6 feet to try to attract more customers. Find the area of the new poster. 2 ft 4 ft 19. Rug Costs You are comparing the two rugs shown below. You want to be sure that the large rug is priced fairly. The price of the small rug is $4. The price of the large rug is $210. a. What are the areas of the two rugs? What is the ratio of the area of the small rug to the area of the large rug? b. Compare the rug costs. Do you think the large rug is a good buy? Explain. 5 ft 10 ft ft 12 ft 14 Chapter 11 Resource Book

7 11.4 For use with pages Use the diagram to find the indicated measure. 1. Find the circumference. 2. Find the circumference. 3. Find the radius. r ft 13 in. Find the indicated measure. 4. The exact radius of a circle with circumference 42 meters C cm 5. The exact diameter of a circle with circumference 39 centimeters 6. The exact circumference of a circle with diameter 15 inches 7. The exact circumference of a circle with radius 27 feet Find the length of C B.. 6 cm P 60 B 9. B P 1 in. C 30 P 2 ft B In ( D shown below, EDF > FDG. Find the indicated measure. E H D 0 7 m G F 11. m C EFG 12. m C EHG 14. Length of C EHG 15. m C EHF 13. Length of C EFG 16. Length of C FEG Find the indicated measure. 17. m C B 1. Circumference of ( F 19. Radius of ( J 12 in. C 23. in ft 290 F D E H cm 55 G J B Chapter 11 Resource Book 149

8 11.4 continued For use with pages Find the perimeter of the region in. 5 mm 11 in. 11 in. 22. In the table below, C B refers to the arc of a circle. Complete the table. 41 in. Radius m C B Length of C B Bicycles The chain of a bicycle travels along the front and rear sprockets, as shown. The circumference of each sprocket is given. 10 in rear sprocket C 5 12 in. 10 in. front sprocket C 5 20 in. a. bout how long is the chain? b. On a chain, the teeth are spaced in } 1 inch intervals. bout how many teeth are 2 there on this chain? 24. Enclosing a Garden You have planted a circular garden adjacent to one of the corners of your garage, as shown. You want to fence in your garden. bout how much fencing do you need? 12 ft 150 Chapter 11 Resource Book

9 FOCUS ON 11.4 For use with pages Tell whether the following postulates in Euclidean geometry are also true in spherical geometry. Draw a diagram to support your answer. 1. Through any two points there exists exactly one line. 2. If two lines intersect, then their intersection is exactly one point. 3. Protractor Postulate: OB and a point on one side OB. The rays of the O can be matched one to one with the real numbers from 0 to 10. The measure of aob is equal to the absolute value of the difference between the real numbers O and 4. ngle ddition Postulate: If P is in the interior of arst, then marst 5 marsp 1 mapst. 5. The following statement is true in Euclidean geometry: Two distinct lines have at most one point of intersection. Rewrite this statement to be true for lines on a sphere. Use the diagram and the given arc measure to find the distances between points and B. Leave your answers in terms of π. 6. m C B m C B m C B m C B m C B m C B Challenge In Euclidean geometry, a polygon with two sides does not exist. Does a two-sided polygon exist in spherical geometry? Draw a diagram to support your answer. Chapter 11 Resource Book 151

10 11.5 For use with pages Find the exact area of the circle. Then find the area to the nearest hundredth in ft cm Find the indicated measure. 4. The area of a circle is 173 square inches. Find the radius. 5. The area of a circle is 290 square meters. Find the radius. 6. The area of a circle is 654 square centimeters. Find the diameter. 7. The area of a circle is 52 square feet. Find the diameter. Find the areas of the sectors formed by CB.. D 4 in. 65 C B B C 27 cm D D B C 1 m Use the diagram to find the indicated measure. 11. Find the area of ( H. 12. Find the radius of ( H. 13. Find the diameter of ( H. G H 0 E ft 2 F G H 9 F E in. 2 The area of ( R is square inches. The area of sector PRQ is 55 square inches. Find the indicated measure. F E 51 H G m Radius of ( R 15. Circumference of ( R P 16. m C PQ 17. Length of C PQ R 1. Perimeter of shaded region 19. Perimeter of unshaded region T 152 Chapter 11 Resource Book

11 11.5 continued For use with pages Find the area of the shaded region cm in m 3.5 m ft 2 ft cm 6 in. 26. Fountain circular water fountain has a diameter of 42 feet. Find the area of the fountain. 27. Landscaping The diagram below shows the area of a lawn covered by a water sprinkler. 16 ft 135 a. What is the area of the lawn that is covered by the sprinkler? b. The water pressure is weakened so that the radius is 10 feet. What is the area of lawn that will be covered? 2. Window Design The window shown is in the shape of a semicircle. Find the area of the glass in the shaded region m 3 m Chapter 11 Resource Book 153

12 11.6 For use with pages Find the measure of a central angle of a regular polygon with the given number of sides. Round answers to the nearest tenth of a degree, if necessary sides sides sides sides Find the given angle measure for the regular dodecagon shown. 5. m TWU 6. m TWX V J U K 7. m XUW. m TWK X T L 9. m UWK 10. m XWK S W M 11. Multiple Choice Which expression gives the apothem for a regular nonagon with side length 10.5? R P N. a 5 C. a } tan } tan 20 B. a } tan 20 D. a p tan regular hexagon has diameter 22 inches. What is the length of its apothem? Round your answer to the nearest tenth. 13. regular octagon has diameter.5 feet. What is the length of its apothem? Round your answer to the nearest tenth. Find the perimeter and area of the regular polygon. Round answers to the nearest tenth, if necessary What is the area of a regular 1-gon with a side length of meters? Round your answer to the nearest tenth, if necessary. 154 Chapter 11 Resource Book

13 11.6 continued For use with pages What is the area of a regular 24-gon with a side length of 10 inches? Round your answer to the nearest tenth, if necessary. 22. What is the area of a regular 30-gon with a radius of 20 feet? Round your answer to the nearest tenth, if necessary. 23. Find the area of a regular pentagon inscribed in a circle whose equation is given by (x 2 4) 2 1 (y 2 6) Find the area of a regular octagon inscribed in a circle whose equation is given by (x 2 2) 2 1 (y 1 3) Find the area of the shaded region. Round answers to the nearest tenth, if necessary In Exercises 29 and 30, use the following information. Tiles You are tiling the floor of a hallway with tiles that are regular hexagons as shown. 29. What is the area of each tile? 30. The hallway has a width of 5 feet and a length of 12 feet. t least how many tiles will you need? 31. cup saucer is shaped like a regular decagon with a diameter of 5.5 inches as shown. a. What is the length of the apothem of the saucer? Round your answer to the nearest tenth. b. What is the perimeter and area of the saucer? Round your answers to the nearest tenth. 6 in. 5.5 in. Chapter 11 Resource Book 155

14 11.7 For use with pages Find the probability that a point K, selected randomly on } E, is on the given segment. Express your answer as a fraction, decimal, and percent. B C D E } BC 2. } BD 3. } CE 4. } D Find the probability that a randomly chosen point in the figure lies in the shaded region Find the probability that a point chosen at random on the segment satisfies the inequality x x x x 2 12 Use the scale drawing. 15. What is the approximate area of the shaded figure in the scale drawing? 16. Find the probability that a randomly chosen point lies in the shaded region. 17. Find the probability that a randomly chosen point lies outside of the shaded region. 1. Boxes and Buckets circular bucket with a diameter of 1 inches is placed inside a two foot cubic box. small ball is thrown into the box. Find the probability that the ball lands in the bucket. 156 Chapter 11 Resource Book

15 11.7 continued For use with pages In Exercises 19 and 20, use the following information. rcs and Sectors The figure to the right shows a circle with a sector that intercepts an arc of Find the probability that a randomly chosen point on the circle lies on the arc. 20. Find the probability that a randomly chosen point in the circle lies in the sector. 60 Find the probability that a randomly chosen point in the figure lies in the shaded region Multiple Choice point X is chosen at random in region, and includes region B and region C. What is the probability that X is not in B?. B. C. rea of 1 rea of C }} rea of rea of 1 rea of C 2 rea of B }}} rea of 1 rea of C rea of 2 rea of B }} rea of 25. Subway t the local subway station, a subway train is scheduled to arrive every 15 minutes. The train waits for 2 minutes while passengers get off and on, and then departs for the next station. What is the probability that there is a train waiting when a pedestrian arrives at the station at a random time? In Exercises 26 2, use the following information. School Day The school day consists of six block classes with each being 60 minutes long. Lunch is 25 minutes. Transfer time between classes and/or lunch is 3 minutes. There is a fire drill scheduled to happen at a random time during the day. 26. What is the probability that the fire drill begins during lunch? B C 27. What is the probability that the fire drill begins during transfer time? 2. If you are 2 hours late to school, what is the probability that you missed the fire drill? Chapter 11 Resource Book 157