Calculate the area of each figure. Each square on the grid represents a square that is one meter long and one meter wide.

Transcription

1 CH 3 Test Review Boundary Lines: Area of Parallelograms and Triangles Calculate the area of each figure Each square on the grid represents a square that is one meter long and one meter wide 1 You are making a kite out of nylon fabric The height of the kite will be 36 inches and the widest part of the kite will be 24 inches as shown in the diagram How much nylon fabric will you need to make the kite? Write the answer in square inches and square feet The Keystone Effect: Area of a Trapezoid Calculate the area of each trapezoid Each square on the grid represents a square that is one inch long and one inch wide 2 The area of a trapezoid is 209 square yards and the bases are 15 yards and 23 yards What is the height of the trapezoid? 3 The area of a trapezoid is 150 square meters The height is 10 meters and one base is two meters longer than the other base What is each base? 1

2 Signs, Signs, Every Place There Are Signs!: Area of Regular Polygons Calculate the area of each regular polygon A regular heptagon has a side length of 24 inches and an apothem of 249 inches What is the area of the regular heptagon? 7 A stop sign has a perimeter of 160 inches and an apothem of 241 inches What is the area of the stop sign? 8 A regular nonagon has an area of 378 square yards and an apothem of 105 yards What is the length of a side of the regular nonagon 2

3 9 A regular polygon has an area of 10,080 square meters The length of a side of the polygon is 30 meters and the apothem is 56 meters What type of regular polygon is this? Say Cheese!: Area and Circumference of a Circle Calculate the circumference and area of each circle Use 314 to approximate π Each square on the grid represents a square that is one centimeter long and one centimeter wide 10 What is the area of the annulus shown? Use 314 to approximate π Boundary Lines: Area of Parallelograms and Triangles Define each term in your own words 11 parallelogram 12 altitude of a parallelogram 3

4 13 height of a parallelogram 14 altitude of a triangle 15 height of a triangle Boundary Lines:Area of Parallelograms and Triangles Calculate the area of each parallelogram EXAMPLE: 16 A = 8(4) = 32 mi 2 4

5 17 Boundary Lines: Area of Parallelograms and Triangles In each parallelogram, the base, height, or area is unknown Calculate the value of the unknown measure EXAMPLE: A = bh 63 = 9h 7 = h The height is 7 meters 18 5

6 Boundary Lines: Area of Parallelograms and Triangles The base of each triangle is labeled Draw a segment that represents the height of the triangle EXAMPLE:

7 Boundary Lines: Area of Parallelograms and Triangles Calculate the area of each triangle EXAMPLE: A = 1 2 (6)(8) = 1 2 (48) = 24 in

8 Boundary Lines: Area of Parallelograms and Triangles In each triangle, the base, height, or area is unknown Calculate the value of the unknown measure EXAMPLE: A = 1 2 bh 30 = 1 2 (15)h 60 = 15h 4 = h The height of the triangle is 4 meters

9 The Keystone Effect: Area of a Trapezoid Problem Set Calculate the area of each trapezoid Each square on the grid represents a square that is two inches long and two inches wide EXAMPLE: A = 1 2 (8 + 16)10 = 1 (24)(10) = square inches 25 9

10 26 The Keystone Effect: Area of a Trapezoid Calculate the area of each trapezoid with the given dimensions, where h represents the height, b 1 represents the length of a base, and b 2 represents the length of the other base EXAMPLE: h = 2,b 1 = 4,b 2 = 3 A = 1 2 (4 + 3)2 = 1 2 (7)(2) = 7 The area is 7 square units 27 h = 6, b 1 = 5, b 2 = 3 28 h = 5, b 1 = 9, b 2 = 1 29 h = 4, b 1 = 2 3, b 2 =

11 The Keystone Effect: Area of a Trapezoid In each trapezoid, one base, height, or area is unknown Calculate the value of the unknown measure EXAMPLE: A = 1 2 (2 + 4)3 = 1 2 (6)(3) = 9 The trapezoid has an area of 9 square feet

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13 Signs, Signs, Every Place There Are Signs!: Area of Regular Polygons Calculate the area of each regular polygon EXAMPLE: A = 1 2 (8)(63)(6) A = 1512 The area is 1512 square centimeters

14 Say Cheese!: Area and Circumference of a Circle Write the term that best completes each statement concentric circles diameter radius circle irrational number circumference annulus 38 The is the distance around a circle 39 The distance that is equal to one half the diameter of a circle is the 40 The distance across a circle through the center is the 41 A decimal that never repeats or terminates is a(n) 42 are circles that share the same center 43 The is the region bounded by two concentric circles Say Cheese!: Area and Circumference of a Circle Problem Set: Calculate the diameter of each circle EXAMPLE: 44 d = 2r = 2(6) = 12cm 14

15 45 Say Cheese!:Area and Circumference of a Circle Calculate the radius of each circle r = d 2 = 18 2 = 9ft

16 Say Cheese!: Area and Circumference of a Circle Calculate the circumference of each circle given the radius r of the circle Write your answers in terms of π EXAMPLE: r = 8 cm C = 2πr = 2(π)(8) = 16π cm 48 r = 2 cm 49 r = 10 ft 50 r = 42 cm Say Cheese!: Area and Circumference of a Circle Calculate the area of each circle given the radius r of the circle Write your answers in terms of π EXAMPLE: r = 6 m A = πr 2 = π(6 2 ) = 36π m 2 51 r = 4 in 16

17 52 r = 12 cm 53 r = 98 yd Say Cheese!: Area and Circumference of a Circle Calculate the radius of each circle given the circumference C of the circle Write your answers in terms of π EXAMPLE: C = 90π mm C = 2πr 90π = 2πr 45 = r r = 45 mm 54 C = 220π ft 55 C = 13π cm 56 C = 108π mi 17

18 Say Cheese!: Area and Circumference of a Circle Calculate the radius of each circle given the area A of the circle Write your answers in terms of π EXAMPLE: A = 9π cm 2 A = πr 2 9π = r 2 9 = r 2 3 = r r = 3 cm 57 A = 16π m 2 58 A = 49π yd 2 59 A = 1 4 π m2 18

19 Say Cheese!: Area and Circumference of a Circle Use the given information to answer each question EXAMPLE: If a circle has a circumference of 6π inches, what is its area? C = 2πr 6π = 2πr 3 = r A = πr 2 A = π(3 2 ) A = 9π The area of the circle is 9π square inches 60 If a circle has a circumference of 3π feet, what is its area? 61 If a circle has an area of 25π square feet, what is its circumference? 19

20 Say Cheese!: Area and Circumference of a Circle Calculate the area of each annulus shown Use 314 to approximate π EXAMPLE: Area of larger circle: A = πr 2 = π(12 2 ) = 144π in 2 Area of smaller circle: A = πr 2 = π(8 2 ) = 64π in 2 Area of annulus: A = 2512 in

21 Installing Carpeting and Tile: Area and Perimeter of Composite Figures Calculate the area of each figure All measurements are in centimeters Use 314 for π and round decimal answers to the nearest hundredth EXAMPLE: A = 14(2) + 7(3) = = 49 cm

22 66 Installing Carpeting and Tile: Area and Perimeter of Composite Figures Calculate the area of the shaded portion of each figure All measurements are in inches Use 314 for π and round decimal answers to the nearest hundredth EXAMPLE: A 3 4 (314)(32 ) = 3 4 (314)(9) = 2120 in

23 All of the line segments in the figure are either vertical or horizontal Determine the perimeter of the figure 23

24 Determine the area of the region bounded by the line segments All of the line segments in the figure shown are either vertical or horizontal What is the perimeter of the figure? 73 All of the line segments in the diagram of the bathroom floor shown are either vertical or horizontal How many one-inch square tiles would it take to tile the entire floor? 24

25 ID: A CH 3 Test Review Answer Section 1 ANS: Area of left triangle = 1 (36)(12) = 216 square inches 2 Area of right triangle = 1 (36)(12) = 216 square inches 2 Totalarea of kite = = 432 square inches 432 square inches 1 square foot 144 square inches = 3 square feet You will need 432 square inches, or 3 square feet, of nylon fabric to make the kite PTS: 1 REF: Ch32 TOP: Assignment 2 ANS: 209 = 1 ( )h = 19h 11 = h The height of the trapezoid is 11 yards PTS: 1 REF: Ch33 TOP: Assignment 3 ANS: Let x represent one base Then x + 2 represents the other base 150 = 1 (x + x + 2)(10) = 5(2x + 2) 150 = 10x = 10x 14 = x One base is 14 meters and the other base is = 16 meters PTS: 1 REF: Ch33 TOP: Assignment 4 ANS: A = 1 2 (18)(124)(5) = 558 square feet PTS: 1 REF: Ch34 TOP: Assignment 1

26 ID: A 5 ANS: A = 1 2 (35)(539)(10) = square centimeters PTS: 1 REF: Ch34 TOP: Assignment 6 ANS: A = 1 2 (24)(249)(7) = The area of the regular heptagon is square inches PTS: 1 REF: Ch34 TOP: Assignment 7 ANS: A = 1 2 (160)(241) = 1928 The area of the stop sign is 1928 square inches PTS: 1 REF: Ch34 TOP: Assignment 8 ANS: 378 = 1 2 ( )(105)(9) 378 = = The length of a side of the regular nonagon is 8 yards PTS: 1 REF: Ch34 TOP: Assignment 9 ANS: 10,080 = 1 2 (30)(56)(n) 10,080 = 840n 12 = n The regular polygon has 12 sides Therefore, the polygon is a regular 12-gon PTS: 1 REF: Ch34 TOP: Assignment 2

27 ID: A 10 ANS: Area of larger circle: A = πr 2 = π(10 2 ) = 100π 314 m 2 Area of smaller circle: A = πr 2 = π(75 2 ) = 5625π m 2 Area of annulus: A = m 2 The area of the annulus is approximately square meters PTS: 1 REF: Ch35 TOP: Assignment 11 ANS: A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel PTS: 1 REF: Ch32 TOP: Skills Practice 12 ANS: An altitude of a parallelogram is a line segment drawn from a vertex, perpendicular to the line containing the opposite side PTS: 1 REF: Ch32 TOP: Skills Practice 13 ANS: A height of a parallelogram is the perpendicular distance from any point on one side to the line containing the opposite side PTS: 1 REF: Ch32 TOP: Skills Practice 14 ANS: An altitude of a triangle is a line segment drawn from a vertex perpendicular to the line containing the opposite side PTS: 1 REF: Ch32 TOP: Skills Practice 15 ANS: A height of a triangle is the perpendicular distance from a vertex to the line containing the base of the triangle PTS: 1 REF: Ch32 TOP: Skills Practice 16 ANS: A = 11(6) = 66 mi 2 PTS: 1 REF: Ch32 TOP: Skills Practice 17 ANS: A = 7(16) = 112 yd 2 PTS: 1 REF: Ch32 TOP: Skills Practice 3

28 ID: A 18 ANS: A = bh 96 = 12b 8 = b The base is 8 feet PTS: 1 REF: Ch32 TOP: Skills Practice 19 ANS: PTS: 1 REF: Ch32 TOP: Skills Practice 20 ANS: PTS: 1 REF: Ch32 TOP: Skills Practice 21 ANS: A = 1 2 (7)(7) = 1 (49) = 245 ft2 2 PTS: 1 REF: Ch32 TOP: Skills Practice 4

29 ID: A 22 ANS: A = 1 2 (45)(4) = 1 (18) = 9 m2 2 PTS: 1 REF: Ch32 TOP: Skills Practice 23 ANS: A = 1 2 bh A = 1 2 (3)(2) A = 1 2 (6) A = 3 The area of the triangle is 3 square feet PTS: 1 REF: Ch32 TOP: Skills Practice 24 ANS: A = 1 2 bh 6 = 1 2 b(3) 12 = 3b 4 = b The base of the triangle is 4 yards PTS: 1 REF: Ch32 TOP: Skills Practice 25 ANS: A = 1 2 (4 + 8)6 = 1 (12)(6) = square inches PTS: 1 REF: Ch33 TOP: Skills Practice 26 ANS: A = 1 2 ( )14 = 1 (30)(14) = square inches PTS: 1 REF: Ch33 TOP: Skills Practice 5

30 ID: A 27 ANS: A = 1 2 (5 + 3)6 = 1 (8)(6) = 24 2 The area is 24 square units PTS: 1 REF: Ch33 TOP: Skills Practice 28 ANS: A = 1 2 (9 + 1)5 = 1 (10)(5) = 25 2 The area is 25 square units PTS: 1 REF: Ch33 TOP: Skills Practice 29 ANS: A = 1 Ê ˆ Ë Á 3 4 = 1 2 (2)(4) = 4 The area is 4 square units PTS: 1 REF: Ch33 TOP: Skills Practice 30 ANS: 1 2 (b + 3)2 = 8 1 b = 8 b 1 = 5 The trapezoid has a base of 5 centimeters PTS: 1 REF: Ch33 TOP: Skills Practice 31 ANS: 1 2 (b 1 + 8)5 = 25 b = 10 b 1 = 2 The trapezoid has a base of 2 yards PTS: 1 REF: Ch33 TOP: Skills Practice 32 ANS: 1 (5 + 15)h = h = 70 h = 7 The trapezoid has a height of 7 yards PTS: 1 REF: Ch33 TOP: Skills Practice 6

31 ID: A 33 ANS: A = 1 2 ( )5 = 1 (35)(5) = The trapezoid has an area of 875 square feet PTS: 1 REF: Ch33 TOP: Skills Practice 34 ANS: 1 2 (b )7 = 98 b = 28 b 1 = 15 The trapezoid has a base of 15 meters PTS: 1 REF: Ch33 TOP: Skills Practice 35 ANS: A = 1 2 (12)(83)(5) = 249 The area is 249 square feet PTS: 1 REF: Ch34 TOP: Skills Practice 36 ANS: A = 1 2 (10)(104)(7) = 364 The area is 364 square yards PTS: 1 REF: Ch34 TOP: Skills Practice 37 ANS: A = 1 2 (4)(75)(12) = 180 The area is 180 square inches PTS: 1 REF: Ch34 TOP: Skills Practice 38 ANS: circumference PTS: 1 REF: Ch35 TOP: Skills Practice 39 ANS: radius PTS: 1 REF: Ch35 TOP: Skills Practice 40 ANS: diameter PTS: 1 REF: Ch35 TOP: Skills Practice 7

32 ID: A 41 ANS: irrational number PTS: 1 REF: Ch35 TOP: Skills Practice 42 ANS: concentric circles PTS: 1 REF: Ch35 TOP: Skills Practice 43 ANS: annulus PTS: 1 REF: Ch35 TOP: Skills Practice 44 ANS: d = 2r = 2(22) = 44ft PTS: 1 REF: Ch35 TOP: Skills Practice 45 ANS: d = 2r = 2(975) = 195 in PTS: 1 REF: Ch35 TOP: Skills Practice 46 ANS: r = d 2 = = 50m PTS: 1 REF: Ch35 TOP: Skills Practice 47 ANS: r = d 2 = 105 = 525 yd 2 PTS: 1 REF: Ch35 TOP: Skills Practice 48 ANS: C = 2πr = 2(π)(2) = 4π cm PTS: 1 REF: Ch35 TOP: Skills Practice 49 ANS: C = 2πr = 2(π)(10) = 20π ft PTS: 1 REF: Ch35 TOP: Skills Practice 50 ANS: C = 2πr = 2(π)(42) = 84π cm PTS: 1 REF: Ch35 TOP: Skills Practice 51 ANS: A = πr 2 = π(4 2 ) = 16π in 2 PTS: 1 REF: Ch35 TOP: Skills Practice 52 ANS: A = πr 2 = π(12 2 ) = 144π cm 2 PTS: 1 REF: Ch35 TOP: Skills Practice 8

33 ID: A 53 ANS: A = πr 2 = π(98 2 ) = 9604π yd 2 PTS: 1 REF: Ch35 TOP: Skills Practice 54 ANS: C = 2πr 220π = 2πr 110 = r r = 110 ft PTS: 1 REF: Ch35 TOP: Skills Practice 55 ANS: C = 2πr 13π = 2πr 65 = r r = 65 cm PTS: 1 REF: Ch35 TOP: Skills Practice 56 ANS: C = 2πr 108π = 2πr 54 = r r = 54 mi PTS: 1 REF: Ch35 TOP: Skills Practice 57 ANS: A = πr 2 16π = πr 2 16 = r 2 4 = r r = 4 m PTS: 1 REF: Ch35 TOP: Skills Practice 9

34 ID: A 58 ANS: A = πr 2 49π = πr 2 49 = r 2 7 = r r = 7 yd PTS: 1 REF: Ch35 TOP: Skills Practice 59 ANS: A = πr π = πr = r2 1 2 = r r = 1 2 m PTS: 1 REF: Ch35 TOP: Skills Practice 60 ANS: C = 2πr A = πr 2 3π = 2πr A = π(15 2 ) 15 = r A = 225π The area of the circle is 225π square feet PTS: 1 REF: Ch35 TOP: Skills Practice 61 ANS: A = πr 2 C = 2πr 25π = πr 2 25 = r 2 C = 2π(5) C = 10π 5 = r The circumference of the circle is 10π feet PTS: 1 REF: Ch35 TOP: Skills Practice 10

35 ID: A 62 ANS: Area of larger circle: A = πr 2 = π(22 2 ) = 484π ft 2 Area of smaller circle: A = πr 2 = π(11 2 ) = 121π ft 2 Area of annulus: A = ft 2 PTS: 1 REF: Ch35 TOP: Skills Practice 63 ANS: Area of larger circle: A = πr 2 = π(34 2 ) = 1156π m 2 Area of smaller circle: A = πr 2 = π(272 2 ) = 73984π m 2 Area of annulus: A = m 2 PTS: 1 REF: Ch35 TOP: Skills Practice 64 ANS: A = 1 2 ( )(15) (20)(15) = = 4875 cm 2 PTS: 1 REF: Ch36 TOP: Skills Practice 65 ANS: Ê A = 2 1 ˆ + 4(1) Ë Á 2 (1)(2) = = 6 cm 2 PTS: 1 REF: Ch36 TOP: Skills Practice 66 ANS: A = 1 2 (6)(4) (5)(10) = = 37 cm 2 PTS: 1 REF: Ch36 TOP: Skills Practice 11

36 ID: A 67 ANS: A 8(5) 1 2 (314)(252 ) = = 3019 in 2 PTS: 1 REF: Ch36 TOP: Skills Practice 68 ANS: A = 3 Ê (32)(277) ˆ Ë Á = 3 4 (4432) = 3324 in 2 PTS: 1 REF: Ch36 TOP: Skills Practice 69 ANS: A 20(20) (314)(10 2 ) = = 86 in 2 PTS: 1 REF: Ch36 TOP: Skills Practice 70 ANS: The perimeter is = 40 centimeters PTS: 1 REF: Ch36 TOP: Mid Ch Test 71 ANS: To determine the area, you can add the areas of the two rectangles One rectangle is 11 units by 12 units and the other rectangle is 10 units by 6 units Total area = 11(12) + 10(6) = = 192 The area of the region bounded by the line segments is 192 square units PTS: 1 REF: Ch36 TOP: End Ch Test 72 ANS: The sum of the shorter horizontal segments is 20 yards, and the sum of the shorter vertical segments is 18 yards So, = 76 The perimeter is 76 yards PTS: 1 REF: Ch36 TOP: End Ch Test 12

37 ID: A 73 ANS: First, calculate the sum of the areas of the two rectangles:7(6) + 5(9) = = 89 square feet Then, multiply the number of square feet by 144, the number of square inches in one square foot: = 12,816 So, 12,816 one-inch square tiles are needed to tile the entire floor PTS: 1 REF: Ch36 TOP: End Ch Test 13