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Area of Figures – Chapter Problems

Area of RectanglesClasswork1. Find the area of a rectangle that has a length of 4.6 in. and a width of 3.4 in.

2. Annabelle wants to place new carpeting in her dining room. Her dining room is a rectangle with a length of 30 feet and a width of 15 feet. a. How much carpeting does she need to buy to cover her entire dining room?b. If the carpeting costs $7.50 per square foot, how much will it cost to carpet

Annabelle’s dining room?

3. The diagonal of a rectangle is 26 feet, and its width is 10 feet. Find the length of the rectangle and its area.

4. The diagonal of a rectangle is 50 feet, and its length is 10 more feet than its width. Find the rectangle’s length, width, and area.

PARCC-type Question5. The population density is the amount of people living per square mile. If the town of

Mathville is a rectangular town that has a length of 12 miles, a width of 6 miles, and a population of 3,982 people, what is the population density of the town? Round your answer to the nearest hundredth.

Area of RectanglesHomework6. Find the area of a rectangle that has a length of 8.5 cm and a width of 3.7 cm.

7. Rick wants to place new carpeting in his living room. His living room is a rectangle with a length of 40 feet and a width of 20 feet.a. How much carpeting does he need to buy to cover his entire living room?b. If the carpeting costs $8.75 per square foot, how much will it cost to carpet Rick’s

living room?

8. The diagonal of a rectangle is 30 feet, and its width is 6 feet less than its length. Find the rectangle’s length, width, and area.

9. A rectangle has a perimeter of 200 feet and its length is 4 times its width. Find the rectangle’s length, width, and area.

PARCC-type Question10.The population density is the amount of people living per square mile. If the town of

Algebraville is a rectangular town that has a length of 13 miles, a width of 10 miles, and a population of 12,576 people, what is the population density of the town? Round your answer to the nearest hundredth.

Geometry – Area of Figures ~1~ NJCTL.org

Area of TrianglesClassworkFind the area of the triangle for #11-14.11. 12.

55°13

12

13. 14.

8

14 14

15.Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an altitude from vertex B perpendicular to the opposite side.

b

a c

B

C A


70°48°

18

14

55°

47°

12

8

73.4 °

100°43°16

22

Area of TrianglesHomeworkFind the area of the triangle for #16-19.16. 17.

30°23

1845°

37°

10

16

18. 19.

20.Derive the formula A = ½ ac sin(B) for the area of a triangle by drawing an altitude from vertex A perpendicular to the opposite side.

a c

bC

B

A


8

10 10

66.42 °

Law of SinesClassworkSolve the triangle. Round your answers to the nearest hundredth.21.

m∠ A=¿__________, m∠B=¿ __________, AC = __________

22.

m∠E=¿__________, m∠F=¿ __________, DF = __________

23.

x = __________, y = __________, z = __________

24.

x = __________, y = __________, z = __________


Law of SinesHomeworkSolve the triangle. Round your answers to the nearest hundredth.25.

m∠H=¿__________, m∠ I=¿ __________, GH = __________

26.

m∠ J=¿__________, m∠L=¿ __________, KL = __________

27.

x = __________, y = __________, z = __________

28.

x = __________, y = __________, z = __________


Area of ParallelogramsClasswork29.Find the area of a parallelogram that has a base of 3.6 inches and a height of 8.2

inches.

30.A parallelogram has a height of 5.2 cm and an area of 48.88 cm2. Find the length of its base.

31.A parallelogram has a base length of 9.3 inches and an area of 56.73 ¿2. Find the height of the parallelogram.

32.A parallelogram has a base length of 7.5 cm. The length of its other side is 5 cm, and the obtuse angle between two of the sides is 133°. Find the height and area of the parallelogram.

33.A diagonal parking space creates a parallelogram. Its length is 21 feet. Its distance along the curb is 10.5 feet, and the acute angle that is made with the curb is 60°. Find the area of the parking space.

34.A window frame is in the shape of a parallelogram. Its base is 4 feet long and its other side length is 3 feet long. The acute angle between two of the sides is 48°. Find the height and the area of the window.

35.Mrs. Polygon is making a quilt for her granddaughter. The quilt is created by stitching together parallelograms that are different colors. Each parallelogram is 3 inches long, its other side is 2 inches long, and the obtuse angle between the two sides is 145°.

a. What is the area of each parallelogram used to make the quilt? Round your answer to the nearest hundredth.

b. The quilt requires 6 parallelograms horizontally and 12 parallelograms vertically. How much material will Mrs. Polygon need to make the quilt?

Area of ParallelogramsHomework36.Find the area of a parallelogram that has a base of 2.5 feet and a height of 7.9 feet

37.A parallelogram has a height of 4.8 cm and an area of 32.16 cm2. Find the length of its base.

38.A parallelogram has a base length of 19.5 inches and an area of 232.05 ¿2. Find the height of the parallelogram.


39.A parallelogram has a base length of 8.3 cm. The length of its other side is 6.2 cm, and the acute angle between two of the sides is 48°. Find the height and area of the parallelogram.

40.A diagonal parking space creates a parallelogram. Its length is 19 feet 10 inches. Its distance along the curb is 12 feet 9 inches, and the acute angle that is made with the curb is 45°. Find the area of the parking space.

41.A window frame is in the shape of a parallelogram. Its base is 3.5 feet long and its other side length is 2.5 feet long. The obtuse angle between two of the sides is 127°. Find the height and the area of the window.

42. In the Polygon household, the living room floor is shaped like a parallelogram. The length of the room is 30 meters and the length of the side adjacent to the base is 20 meters. The obtuse angle between the two sides is 125°. Mrs. Polygon wants to install hardwood flooring in her living room.

a. What is the area of the living room?

b. If hardwood flooring costs $8.25 per square foot, how much will it cost to get the hardwood floor installed?

Area of Regular PolygonsClassworkCalculate the perimeter and area of each regular polygon. Round your answers to the nearest hundredth.43.

44.


45.

46.

Area of Regular PolygonsHomeworkCalculate the perimeter and area of each regular polygon. Round your answers to the nearest hundredth.47.

48.


49.

50.

Area of Circles & SectorsClassworkFind the area of the minor sector. Round to the nearest hundredth or leave your answer in terms of π.51. 52. 53. 54.

Find the area of the major sector. Round to the nearest hundredth or leave your answer in terms of π.55. 56. 57. 58.


R=3in450

220o

R=6ft. 100o r=10 cm 95o

d=15 in

R=3in450 220o

R=6ft.95o

d=15 in

100o r=10 cm

Area of Circles & SectorsHomeworkFind the area of the minor sector. Round to the nearest hundredth or leave your answer in terms of π.59. 60. 61. 62.

Find the area of the major sector. Round to the nearest hundredth or leave your answer in terms of π.63. 64. 65. 66.

Area of Other QuadrilateralsClassworkAnswer each question below.67. A teacher has 15 desks in their classroom. Each desk was created using wood for

the flat top surface and metal bars for the legs. The shape of all of the flat top surfaces is an isosceles trapezoid. The short and long bases have a length of 3 feet and 5 feet, respectively, and the acute angle formed by the legs and the long base is 68°. a. Find the height of the trapezoid.

b. Find the total amount of wood required to make all 15 desks in the classroom.

68. A ruby was cut into the shape of a kite to make the ring shown to the right. If its diagonals measure 20 mm and 11 mm, what is the area of the stone?


115o

d=10ft. r=6.7 m

105o74o

r=2.3 cmd=21in

47o

115o

d=10ft. r=6.7 m

105o74o

r=2.3 cmd=21in

47o

69.A rhombic triacontahedron is a convex 3-D solid with 30 rhombic faces. Each rhombic face has acute angles that measure 63.43°. The length of the small diagonal is 2 inches.

a. Find the length of the long diagonal in the rhombus.

b. Find the area of one rhombic face.

c. Find the surface area (area of all of the faces) in this rhombic triacontahedron.

Find the area of each complex figure given below.70. 71. The radius of each semicircle is 5 cm.

PARCC-type QuestionsSolve the following word problems based on the information below.

The Bisect Building Company has created a building plan for the new patio for the Quadrilateral Family, shown in the figure.

72.The roof of the patio made from 2 isosceles trapezoids and 3 rectangles. a. What is the area of the entire roof? Explain your answer.

b. Each bundle of shingles covers 36 ft2. Shingles cost $25.50 per bundle and must be purchased in full bundles. The builder has a budget of $125 for shingles. Did the Bisect Building Company budget enough money for the shingles? Explain your answer.


73. The patio will cover the Quadrilateral’s new hot tub (or Jacuzzi tub) and possibly a sidewalk that is 2 feet wide on all four sides. The hot tub is 6’ 10” x 6’ 10”.a. How much concrete is needed to make the sidewalk surrounding the entire hot

tub (or Jacuzzi tub)? Explain your answer.

b. If the price for sidewalk installation is $4.75 per square foot, how much will the Quadrilateral’s have to pay to get their sidewalk installed? Explain your answer.

c. Will the roof cover the hot tub (or Jacuzzi tub) and the sidewalk? Explain your answer.

Area of Other QuadrilateralsHomeworkAnswer each question below.74.A teacher has 12 desks in their classroom. Each desk was created using wood for

the flat top surface and metal bars for the legs. The shape of all of the flat top surfaces is an isosceles trapezoid. The short and long bases have a length of 3.5 feet and 5.5 feet, respectively, and the acute angle formed by the legs and the long base is 57°.

a. Find the height of the trapezoid.

b. Find the total amount of wood required to make all 12 desks in the classroom.

75.The logo for Mitsubishi Motors is comprised of 3 congruent rhombi joined together at a center point to create a triangular figure. In each rhombus, the length of the long diagonal is 5 inches and the length of the short diagonal is 2.5 inches.

a. What is the area of each rhombus in the logo?

b. What is the total rhombus area of the logo?

76.A blue sapphire stone was cut into the shape of a kite to make a necklace as shown to the right. If its diagonals measure 2.2 cm and 1.1 cm, what is the area of the stone?


Find the area of each complex figure given below.77. 78.

PARCC-type QuestionsSolve the following word problems based on the information below.

Mrs. Skew is going to redesign her bedroom, shown in the picture to the right.

79.The first thing that she needs to do is replace her carpet. If carpet is sold for $6.75 per square foot, how much will it cost? Explain your answer.

80.Mrs. Skew is going to paint all of the walls, which are 8 feet high, with a 2 coats of paint. The room contains a doorway that is 3 ft by 7 ft, 3 windows measuring 4 ft by 3.5 ft, and a closet doorway that is 6 ft by 7 ft. The doorway, windows and closet doorway will not be painted.a. What is the total amount of wall space needs to be covered with paint? Explain

your answer.

b. If paint is sold in 1-gallon containers, and each gallon of paint covers 350 square feet and each can of paint costs $12.50, how much money does Mrs. Skew need to spend on paint? Explain your answer.


81.Given the figure below, explain why the area formula for a kite is A=12d1d2.

Area and Perimeter of Figures in the Coordinate PlaneClassworkCalculate the perimeter & area of each figure below.82. 83.

PARCC-type Questions:84.The figure shows polygon ABCDEF in the coordinate

plane with point A at (0, 3.71), point B at (1.64, 3.71), point C at (1.64, 3), point D at (2.89, 3), point E at (2.89, 0), and point F at the origin. Polygon ABCDEF can be used to approximate the size of the state of Utah with x and y scales representing hundreds of miles.a. Based on the information given, how many miles is

the perimeter of Utah?

b. At the end of 2010, the population of Utah was 2,763,885 people. Based on the information given, what was the population density at the end of 2010?


85.The town of Geometryville has Polygon Park on a plot of land. The figure represents a map of the Polygon Park showing the location of the Parking Area, Soccer Fields, and Playground. The coordinates represent points on a rectangular grid with the units in hundreds of feet. a. There is a walking trail around

the entire park, including the Parking area. What is the length of the walking trail? Express your answer to the nearest foot.

b. What is the area of the plot of land that does not include the parking area? Express your answer to the nearest square foot.

c. The town is planning to put a fence around the Playground and Soccer Fields. What is the total length of fencing needed? Express your answer to the nearest foot.

d. In the future, Geometryville has plans to construct a circular pool centered at (35, 8) on the map. Which of the listed measurements could be the radius of the pool that will fit on the map and be at least 500 feet away from the Soccer Fields and edges of the park. Select all that apply.

i. 150 feetii. 300 feetiii. 450 feet

iv. 600 feetv. 750 feet


Area and Perimeter of Figures in the Coordinate PlaneHomeworkCalculate the perimeter & area of each figure below.86. 87.

PARCC-type Questions:88.The figure shows polygon ABCDEFGH in the

coordinate plane with point A at (0, 3.92), point B at (3.02, 3.92), point C at (3.02, 0.48), point D at (1.42, 0.48), point E at (1.42, 0.35), point F at (0.46, 0.35), point G at (0.46, 0), and point H at the origin. Polygon ABCDEFGH can be used to approximate the size of the state of New Mexico with x and y scales representing hundreds of miles.a. Based on the information given, how

many miles is the perimeter of New Mexico?

b. At the end of 2010, the population of New Mexico was 2,059,179 people. Based on the information given, what was the population density at the end of 2010?


89.The town of Geometryville has a Pentagon Park on a plot of land. The figure represents a map of Pentagon Park showing the location of the Parking Area, Basketball Courts, and Playground. The coordinates represent points on a rectangular grid with the units in feet.

a. There is a walking trail around the entire park, including the Parking area. What is the length of the walking trail? Express your answer to the nearest foot.

b. What is the area of the plot of land that does not include the parking area? Express your answer to the nearest square foot.

c. The town is planning to put a fence around the Playground and Basketball Courts. What is the total length of fencing needed? Express your answer to the nearest foot.

d. In the future, Geometryville has plans to construct a circular pool centered at (150, 165) on the map. Which of the listed measurements could be the diameter of the pool that will fit on the map and be at least 20 feet away from the Basketball Courts and edges of the park. Select all that apply.

i. 50 feetii. 40 feetiii. 30 feet

iv. 20 feetv. 10 feet


Area of Figures – Chapter Review

1. The diagonal of a rectangle is 39 feet, and its length is 21 more feet than its width. Find the rectangle’s length, width, and area.

2. The perimeter of a rectangle is 192 feet. The length of the rectangle is 1 more than quadruple its width. Find the length, width, and area of the rectangle.

3. The population density is the amount of people living per square mile. If the town of Calculusville is a rectangular town that has a length of 27 miles, a width of 13 miles, and a population of 13,479 people, what is the population density of the town?

a. 38.4 people per square mileb. 130.1 people per square milec. 168.5 people per square miled. 537.6 people per square mile

4. Calculate the area of the triangle given below. Round your answer to the nearest hundredth.

Use the diagram of ⊙C to answer questions #5 & 6.5. What is the area of the sector formed by AE, EC, and AC,

when CD=6m and m∠ ACE=55 °?a. 95.82 m2

b. 47.91 m2 c. 34.56 m2 d. 17.28 m2

6. What is the area of the sector formed by ADE, EC, and AC, when CD=6m and m∠ ACE=55 °?

a. 95.82 m2

b. 47.91 m2 c. 34.56 m2 d. 17.28 m2


7. A window frame is in the shape of a parallelogram. Its base is 2.5 feet long and its other side length is 4.5 feet long. The obtuse angle between two of the sides is 113°. What is the area of the window?

a. 26.50 ft2 b. 12.21 ft2

c. 10.36 ft2

d. 4.14 ft2

8. Which formulas below are used to calculate the area of a shape? Select all that apply.

a. bh e. 12aP

b. π r2 f. 2πr

c. 2 l+2w g. 12h(b1+b2)

d.12d1d2 h. 4s

9. The head of a sprinkler has a radius of 15 ft and covers an arc region that measures 135°. How much grass can it water at one time?

10.The state flag of Delaware has a rhombus in its center. The length of the state flag is 38 feet and the width is 20 feet. If the longer diagonal of the rhombus is 2/3 the length of the rectangle and the shorter diagonal is 3/5 the width of the rectangle, what is the area of the rhombus in the flag?

11. The restaurant sign for McDonald’s, shown to the right has the 2 golden arches sitting on an isosceles trapezoid. If the bases are 35 feet and 27 feet respectively and the acute angle formed between the top base and its legs is 70°. What is the area of the red trapezoid in the sign?


Extended Constructed Response – Solve the problems, showing all work. Partial credit may be given. 12. Solve the triangle. Round your answers to the nearest hundredth.

13.Calculate the perimeter and area of the regular polygon shown below. Round your answers to the nearest hundredth, or leave them in simplified radical form.

14.The picture below shows the yard of the Fraction family. The coordinates represent points on a rectangular grid with the units in feet.a. What is the perimeter of their

yard?

b. Every spring, Mr. Fraction fertilizes the lawn. What is the area of it?

c. This year, the Fractions are going to have a fence installed, represented by the red dotted line. Determine the amount of fencing required.

d. In the future, the Fractions want to install a square-shaped pool centered at (150, 75). If the pool must be at least 10 feet away from the house and the fencing, which of the listed measurements could be the area of the pool. Select all that apply.

i. 1,200 ft2 ii. 1050 ft2 iii. 900 ft2 iv. 750 ft2 v. 600 ft2


15. Mrs. Octagon going to redesign her guest bedroom, shown in the picture to the right.a. The first thing that she needs to do is replace

the carpet. If carpet is sold for $5.25 per square foot, how much will it cost? Explain your answer.

b. Mrs. Octagon is going to paint all of the walls, which are 8 feet high, with 2 coats of paint. The room contains a doorway that is 4 feet by 7 feet, 3 windows measuring 3 feet by 4.5 feet, and a closet doorway that is 7 feet by 7 feet. The doorway, windows, and closet doorway will not be painted. What is the total amount of wall space that needs to be covered with paint? Explain your answer.

c. If paint is sold in 1-gallon containers, each gallon of paint covers 350 square feet, and each gallon of paint costs $12.10, how much money does Mrs. Octagon need to spend on paint? Explain your answer.


Answers

1. 15.64 ¿2

2. a) 450 ft2

b) $3,3753. length = 24 ft

Area = 240 ft2

4. x = width = 30 ftlength = 40 ftArea = 1,200 ft2

5. 55.31 people per square mile6. 31.45 cm2

7. a) 800 ft2

b) $7,0008. x = length = 24 ft

width = 18 ftArea = 432 ft2

9. x = width = 20 ftlength = 80 ftArea = 1,600 ft2

10.96.74 people per square mile11. 63.89 sq units12.46.95 sq units13.53.67 sq units14.93.64 sq units15.sin C = h/a

h = a sin CA = (1/2)(base)(height)A = (1/2)b (a sinC)A = (1/2)ab sin C

16.103.5 sq units17.79.22 sq units18.36.66 sq units19.173.33 sq units20.sin B = h/c

h = c sin BA = (1/2)(base)(height)A = (1/2)a (c sinB)A = (1/2)ac sin B

21.m∠ A=57.41 ° ,m∠B=85.59 °, AC = 8.28 units

22.m∠E=31.62 °,m∠F=22.38 °,DF = 11.02 units

23.x = 85°, y = 13.79 units, z = 27.48 units

24.x = 80°, y = 8.79 units, z = 6.53 units

25.m∠H=57.98 ° ,m∠ I=90.02°, GH = 9.44

26.m∠ J=21.4 ° ,m∠L=53.6 °, KL = 4.53

27. x = 99 o, y = 54.26 units, z = 63.19 units

28.x = 40 o, y = 18.60 units, z = 13.20 units

29.29.52 ¿2

30.9.4 cm31.6.1 in32.h = 3.66 cm

A = 27.45 cm2

33.h=5.25√3 ft ≈9.09 ftA=110.25√3 ft2≈190.89 ft2

34.h = 2.23 ftA = 8.92 ft2

35.a) A = 3.45 ¿2

b) Total material = 248.4 ¿2

36.19.75 ft2

37.6.7 cm38.11.9 in.39.h = 4.61 cm

A = 38.26 cm2

40.h = 9.02 ftA = 178.90 ft2

41.h = 2 ftA = 7 ft2

42.A = 491.4 ft2

Cost = $4,054.0543.P = 72 units

A=216√3units2≈374.12units2 44.P=24 √3units≈ 41.57units

A=48√3units2≈83.14 units2

45.P = 73.47 unitsA = 407.29 units2

46.P = 72.65 unitsA = 363.25 units2

47.P = 24 unitsA=24√3units2≈ 41.57units2

48.P = 74.16 units


A = 423.82 units2

49.P = 60 unitsA = 247.74 units2

50.P=24 √2units≈33.94unitsA = 72 units2

51.A = 1.125π in2/3.53 in2

52.A = 14π / 43.98 ft2

53.A = 27.78π / 87.27 cm2

54.A = 53.13π / 166.9 in2

55.A = 7.77π / 24.4 in2

56.A = 22π / 69.12 ft2

57.A = 72.22π / 226.89 cm2

58.A = 112.5π / 353.43 in2

59.A = 18.06π / 56.72 ft2

60.A = 13.09π / 41.13 m2

61.A = 1.09π / 3.42 cm2

62.A = 57.58π / 180.88 in2

63.A = 50π / 157.08 ft2

64.A = 31.8π / 99.89 m2

65.A = 4.2π / 13.2 cm2

66.A = 220.5π / 692.72 in2

67.a) h = 2.48 ftb) A = 148.8 ft2

68.A = 110 mm2

69.a) Long diagonal = 3.24 in.b) A = 3.24 ¿2

c) Total: A = 97.2 ¿2

70.A = 161.25 ¿2 71.A = (100 + 50π ¿cm¿2 = 257.08

cm2

72.a) Sample Answer: Before finding the area of the roof, you need to determine the length of the legs and height in the isosceles trapezoids using trigonometry and the segment addition postulate. Since the top base is 6’ 2.5”, or 74.5”, the bottom base, which is 9’ or 108” in length, can be divided into 3 sections, measuring 16.75”, 74.5” and 16.75” from left to right. Using the 16.75” as your adjacent side

to the 65 degree angle, you can use tangent to calculate the height of the trapezoidh = 16.75tan(65) = 35.92 in.Using the same adjacent side measurement and cosine, you can find the length of each leg in the isosceles trapezoidleg = 16.75/tan(65) = 39.63 in. Using these measurements, you can now determine the total area of the roof.A = 108(39.63)(2) + 74.5(108) + 2(½)(35.92)(74.5 + 108) = 23,161.48 ¿2 ≈ 160.84 ft2

b) Sample Answer: Since 1 bundle of shingles covers and area of 36 ft2, the total bundles that need to be purchased is 160.84/36 = 4.47 ≈ 5 bundles, making the cost $127.50. Since their budget was $125, which is less than $125, they did not budget enough money for the shingles.

73.a) Sample Answer: The dimensions of the square formed by the hot tub and sidewalk are 10’10” by 10’10”, or 130” by 130”, making its area 16,900 ¿2≈117.36 ft2. The dimensions of the hot tub are 6’10” by 6’10” or 82” by 82” making its area 6,724 ¿2≈46.69 ft2. By subtracting these two areas, we calculate that the area of the sidewalk is 10,176 ¿2≈ 70.67ft2

b) Sample Answer: Since the unit price is $4.75 per square foot, the total cost for the sidewalk installation is 4.75(70.67) = $335.68c) Sample Answer: No, the total length of the hot tub & side walk is 10’10” or 130”, which exceeds the 9’ or 108” measurement from


the roof.74.a) h = 1.54 ft

b) A = 83.16 ft2

75.a) A = 6.25 ¿2

b) A = 18.75 ¿2

76.A = 1.21 cm2

77.A = 46.40 cm2

78.A = 632.6 ¿2

79.Sample Answer: The total area of the floor is 5(30) + 27(10) + ½(20.61)(27+6) 150 + 270 + 340.065760.065 ft2

If you take the total area of the floor and multiply it by the unit price of $6.75, then the total cost is $5,130.44.

80.a) Sample Answer: Since all of the walls are rectangular, you can find the complete area of the walls by multiplying the perimeter of the room by the height of the wall, and then subtract the areas that will not be painted (door, windows & closet). Using this method, the total amount of wall space that will be painted isArea of walls: 81(8) = 648 ft2

Area of door: 7(3) = 21 ft2

Area of windows: 3(4)(3.5) = 42 ft2

Area of closet: 6(7) = 42 ft2

Area to be painted: 2(648 – 21 – 42 – 42) = 2(543) = 1,086 ft2

b) Sample Answer: 1,086/350 = 3.10 ≈4 cans of paint are required. Since each can of paint costs $12.50, the total cost for Mrs. Skew will be 4(12.50) = $50.

81.Sample Answer: If you take the bottom right triangle from the kite shown and reflect it vertically, it will fit on the other side of the bottom left triangle. The same can be done to the upper right

triangle: move it and reflect it vertically; then it will fit on the other side of the top left triangle. When this occurs, a rectangle is formed, and the length would be diagonal 2 and the width will be ½ the length of diagonal 1. Therefore the formula for the

area of a kite is A=12d1d2.

Visual Sample Answer:

Figure 1 Figure 2

Figure 3Using the area of a rectangle formula and the dimensions given above in Figure 3, we can conclude that the area of a kite is

A=12d1d2.

82.P = 6√41units≈38.42unitsA = 82 units2

83.P = ( 4√5+10√2 )unitsP ≈23.09unitsA = 30 units2

84.a) 1,320 milesb) 28.10 people per square mile

85.a) 18,110 ftb) 14,250,000 ft2c) 12,781 ftd) i & ii

86.P = (3√17+√85+√34 )unitsP ≈27.42unitsA = 25.5 units2

87.P = (7√13+√26+√85 )units


P ≈38.40unitsA = 45.5 units2

88.a) 1,388 milesb) 19.18 people per square mile

89.a) 857 ftb) A = 35,375 ft2

c) 667 ftd) iii, iv & v

Answers: Chapter Review

1. l=36 ft ,w=15 ft , A=540 ft2

2. l=77 ft ,w=19 ftA=1,463 ft2

3. A4. A = 78.14 m2

5. D6. A7. C8. A, B, D, E, G

9.675π

8ft2=265.07 ft2

10.A = 152 ft2

11. A = 340.69 ft2

12.m∠C=54 ° , BC=13cmAC=4.43cm

13.P=72√3units≈124.71unitsA=648√3units2≈1,122.37units2

14.a) P = 660 ftb) Area of the lawn = 20,200 ft2

c) 525 ft of fencingd) iii, iv, and v

15.a) Sample Answer: The total area of the floor is

12

(10√3 ) (10+30 )+25 (37 )

346.41+9251,271.41 ft2If you take the total area of the floor and multiply it by the unit price of $5.25, then the total cost is

$6,674.90b) Sample Answer: Since all of

the walls are rectangular, you can find the complete area of the

walls by multiplying the perimeter of the room by the height of the

wall, and then subtract the areas that will not be painted (door, windows & closet). Using this

method, the total amount of wall space that will be painted is

Area of walls: 144(8) = 1,152 ft2

Area of door: 7(4) = 28 ft2

Area of windows: 3(4.5)(3) = 40.5 ft2

Area of closet: 7(7) = 49 ft2

Area to be painted: = 1,152 – 28 – 40.5 – 49

= 2,069 ft2

c) Sample Answer: 2,069/350 = 5.91 ≈6cans of paint are required.

Since each can of paint costs $12.10, the total cost for Mrs.

Octagon will be 6(12.10) = $72.60


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