Name: Class: Date: Geometry Chapter 3 Review

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1 Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram and show all your work. 5. The figure shown consists of a rectangle and two congruent circles. If the area of the rectangle is 150 square feet, what is the radius of one of the circles?. Calculate the area of the trapezoid shown.. 6. The area of the triangle shown is 7.36 square inches. What is the value of n? 3. The area of the triangle shown is square centimeters. What is the value of n? 7. The diameter of the large circle is 6 feet. The diameter of the small circle is feet. Calculate the area of the shaded portion. Leave your answer in terms of π. 4. A side length of the square is 14 inches. The diameter of the circle is 8 inches. Calculate the area of the shaded portion. Use 3.14 forπ. 1

2 Name: ID: A 8. The figure shown consists of a rectangle and 10 congruent semicircles. If the perimeter of the rectangle is 88 centimeters, what is the radius of one of the semicircles? 1. All of the line segments in the figure are either vertical or horizontal. Determine the perimeter of the figure. 9. Calculate the area of the region bound by the given coordinates on the graph. Show all your work. 13. A triangle has an area of 15.9 square millimeters. The height of the triangle is 5.3 millimeters. What is the length of the base of the triangle? Explain. 14. The figure shown is made up of three equal-sized equilateral triangles. The combined area of the triangles is 63 square inches. The height of one of the triangles is 3.5 inches. What is the perimeter of the figure? Explain. 10. Draw a rectangle that has a perimeter of 36 centimeters and an area of 65 square centimeters. Include the length and width on the sketch. 11. The area of a parallelogram is 85 square meters and its base is 17 meters long. What is the height of the parallelogram?

3 Name: ID: A 15. Determine the area of the region bounded by the line segments. 17. 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? In each rectangle, the length, width, or area is unknown. Calculate the value of the unknown measure All of the line segments in the figure shown are either vertical or horizontal. What is the perimeter of the figure? Calculate the missing measures using the given measure for each square. 19. Side length: Area: 16 square inches Perimeter: 0. Side length: Area: Perimeter: 36 meters 3

4 Name: ID: A Use the given information to answer each question. 1. Mr. Green is baking a square cake. He plans to frost only the top of the cake. He has enough frosting to cover 144 square inches of cake, and he wants to use all of the icing. What should be the dimensions of the cake? 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 represents the length of the other base. 5. h = 1, b 1 = 10, b = 14. In each parallelogram, the base, height, or area is unknown. Calculate the value of the unknown measure. 6. In each trapezoid, one base, height, or area is unknown. Calculate the value of the unknown measure. 3. Calculate the area of each triangle. 7. Use the given information to answer each question. In each triangle, the base, height, or area is unknown. Calculate the value of the unknown measure. 8. Yvonne cut a picture into the shape of a trapezoid to place into her scrap book. The picture is shown below. What is the area of the picture? 4. 4

5 Name: ID: A 9. Calculate the area of each regular polygon. Calculate the area of each circle given the radius r of the circle. Write your answers in terms of π. 34. r = 1 cm 30. Calculate the radius of each circle given the circumference C of the circle. Write your answers in terms of.π 35. C = 0π ft 36. C = π yd Use the given information to calculate the area of each regular polygon. 31. A regular octagon has a perimeter of 36 millimeters and an apothem length of 5.4 millimeters. What is the area of the regular octagon? Calculate the radius of each circle given the area A of the circle. Write your answers in terms of π. 37. A = 16π m Calculate the circumference of each circle given the radius r of the circle. Write your answers in terms of.π 38. A = 49π yd 3. r = 3 in. Use the given information to answer each question. 33. r = 10 ft 39. If a circle has a circumference of 3π feet, what is its area? 40. If a circle has an area of 4π square meters, what is its circumference? 5

6 Name: ID: A Calculate the area of each annulus shown. Use 3.14 to approximate π Convert the given units. Calculate the area of the shaded portion of each figure. All measurements are in inches. Use 3.14 for π and round decimal answers to the nearest hundredth. Example: Convert 54 square feet into square yards. 54 square feet 1 square yard 9 square feet = 6 square yards Convert 88 square inches into square feet. 43. Convert 6 square feet into square inches. 44. Calculate the area of each figure. All measurements are in centimeters. Use 3.14 for π and round decimal answers to the nearest hundredth. 6

7 Geometry Chapter 3 Review Answer Section 1. ANS: Draw a rectangle. The length of the field is 85 meters because = 85. So, the perimeter of the field is 330 meters because (80) + (85) = 330. PTS: 1 REF: Ch3.1 TOP: Pre Test. ANS: b 1 = 1 cm, b = 0 cm, h = 6 cm A = 1 (b 1 + b )h = 1 (1 + 0)6 = 96 The area of the trapezoid is 96 square centimeters. PTS: 1 REF: Ch3.3 TOP: Pre Test 3. ANS: A = cm, h = 5. cm, b = n A = 1 bh = 1 (n)(5.) 14.8 = n The value of n is PTS: 1 REF: Ch3. TOP: Pre Test 4. ANS: Calculate the areas of the square and circle, then calculate the difference between the areas: A = π square inches. PTS: 1 REF: Ch3.6 TOP: Pre Test 1

8 5. ANS: The length of the rectangle is equal to 4r and the width is equal to r, where r is the radius of one circle. Substitute these values into the formula for the area of a rectangle and solve for r. A = lw 150 = (4r)(r) 150 = 8r 1.5 = r The radius of one of the circles is 1.5 feet. PTS: 1 REF: Ch3.6 TOP: Pre Test 6. ANS: A = 7.36 in., h = n, b = 1.6 in. A = 1 bh 7.36 = 1 (1.6)(n) The value of n is 6.7. PTS: 1 REF: Ch3. TOP: Post Test 7. ANS: Calculate the areas of the small and large circles, then find the difference between the area of the two circles: A = 9π π = 8π square feet. PTS: 1 REF: Ch3.6 TOP: Post Test 8. ANS: There are 10 semicircles. Divide the perimeter of the rectangle by 10 to get the length of each diameter: = 8.8 centimeters. Divide each diameter by to get the length of each radius: 8.8 = 4.4 centimeters. The radius of one of the semicircles is 4.4 centimeters. PTS: 1 REF: Ch3.6 TOP: Post Test 9. ANS: Connect point (6, 0) with point (13, 14) to form two triangles. The area of the large triangle is 1 (13)(14) = 91 square units. The area of the small triangle is 1 (3)(6) = 9 square units. The total area of the region is = 100 square units. PTS: 1 REF: Ch3. TOP: Mid Ch Test

9 10. ANS: Determine two numbers that when multiplied equal 65 and when added and multiplied by equal 36. The product of the numbers 5 and 13 are equal to 65, and when added and multiplied by are equal to 36. PTS: 1 REF: Ch3.1 TOP: Mid Ch Test 11. ANS: The height is = 5 meters. PTS: 1 REF: Ch3. TOP: Mid Ch Test 1. ANS: The perimeter is = 40 centimeters. PTS: 1 REF: Ch3.6 TOP: Mid Ch Test 13. ANS: Substitute 15.9 for A and 5.3 for h into the formula for the area of a triangle. Then solve for b. A = 1 bh 15.9 = 1 (b)(5.3) 6 = b The length of the base of the triangle is 6 millimeters. PTS: 1 REF: Ch3. TOP: Mid Ch Test 14. ANS: First, determine the area of one triangle. Because the triangles are equal-sized, the areas are equal. The area of one triangle is 63 3 = 1 square inches. The length of a side of the triangle is ( 1) 3.5 = 1 inches. The perimeter is made up of 5 equal sides of the triangles, or 5(1) = 60 inches. The perimeter of the figure is 60 inches. PTS: 1 REF: Ch3.6 TOP: Mid Ch Test 15. ANS: To determine the area, you can add the areas of the two rectangles. One rectangle is 11 units by 1 units and the other rectangle is 10 units by 6 units. Total area = 11(1) + 10(6) = = 19 The area of the region bounded by the line segments is 19 square units. PTS: 1 REF: Ch3.6 TOP: End Ch Test 3

10 16. ANS: The sum of the shorter horizontal segments is 0 yards, and the sum of the shorter vertical segments is 18 yards. So, = 76. The perimeter is 76 yards. PTS: 1 REF: Ch3.6 TOP: End Ch Test 17. 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: = 1,816. So, 1,816 one-inch square tiles are needed to tile the entire floor. PTS: 1 REF: Ch3.6 TOP: End Ch Test 18. ANS: A = lw 35 = 7w 5 = w The width is 5 feet. PTS: 1 REF: Ch3.1 TOP: Skills Practice 19. ANS: Side length: 4 inches Perimeter: 16 inches PTS: 1 REF: Ch3.1 TOP: Skills Practice 0. ANS: Side length: 9 meters Area: 81 square meters PTS: 1 REF: Ch3.1 TOP: Skills Practice 1. ANS: Area = side 144 = s 1 = s The cake should be a square with each side 1 inches long. PTS: 1 REF: Ch3.1 TOP: Skills Practice. ANS: A = bh 36 = 18h = h The height is meters. PTS: 1 REF: Ch3. TOP: Skills Practice 4

11 3. ANS: A = 1 (0)(11) = 1 (0) = 110 mm PTS: 1 REF: Ch3. TOP: Skills Practice 4. ANS: A = 1 bh 6 = 1 b(3) 1 = 3b 4 = b The base of the triangle is 4 yards. PTS: 1 REF: Ch3. TOP: Skills Practice 5. ANS: A = 1 ( ) Ê 1 ˆ Ë Á Ê 1 ˆ Ë Á = 6 The area is 6 square units. PTS: 1 REF: Ch3.3 TOP: Skills Practice 6. ANS: 1 (b + 3) = 8 1 b = 8 b 1 = 5 The trapezoid has a base of 5 centimeters. PTS: 1 REF: Ch3.3 TOP: Skills Practice 7. ANS: 1 (1 + 3)h = 5 h = 5 h =.5 The trapezoid has a height of.5 feet. PTS: 1 REF: Ch3.3 TOP: Skills Practice 5

12 8. ANS: A = 1 (b + b )h 1 A = 1 (4 + 7)5 A = 1 (11)(5) A = 7.5 The area of the picture is 7.5 square inches. PTS: 1 REF: Ch3.3 TOP: Skills Practice 9. ANS: A = 1 (0)(4.1)(8) = 198 The area is 198 square kilometers. PTS: 1 REF: Ch3.4 TOP: Skills Practice 30. ANS: A = 1 (4)(7.5)(1) = 180 The area is 180 square inches. PTS: 1 REF: Ch3.4 TOP: Skills Practice 31. ANS: A = 1 (36)(5.4) = 97. The area of the regular octagon is 97. square millimeters. PTS: 1 REF: Ch3.4 TOP: Skills Practice 3. ANS: C = πr = (π)(3) = 6π in. 33. ANS: C = πr = (π)(10) = 0π ft 6

13 34. ANS: A = πr = π(1 ) = 144π cm 35. ANS: C = πr 0π = πr 110 = r r = 110 ft 36. ANS: C = πr π = πr 0.5 = r r = 0.5 yd 37. ANS: A = πr 16π = πr 16 = r 4 = r r = 4 m 38. ANS: A = πr 49π = πr 49 = r 7 = r r = 7 yd 7

14 39. ANS: C = πr A = πr 3π = πr A = π(1.5 ) 1.5 = r A =.5π The area of the circle is.5π square feet. 40. ANS: A = πr C = πr 4π = πr 4 = r C = π() C = 4π = r The circumference of the circle is 4π meters. 41. ANS: Area of larger circle: A = πr = π( ) = 484π ft Area of smaller circle: A = πr = π(11 ) = 11π ft Area of annulus: A = ft 4. ANS: 1 square foot 88 square inches = square feet 144 square inches PTS: 1 REF: Ch3.6 TOP: Skills Practice 43. ANS: 144 square inches 6 square feet = 864 square inches 1 square foot PTS: 1 REF: Ch3.6 TOP: Skills Practice 8

15 44. ANS: A = 1 ( )(15) + 1 (0)(15) = = cm PTS: 1 REF: Ch3.6 TOP: Skills Practice 45. ANS: A = 4(3) + 1 (3.14)( ) = = 18.8 cm PTS: 1 REF: Ch3.6 TOP: Skills Practice 46. ANS: A 0(0) (3.14)(10 ) = = 86 in. PTS: 1 REF: Ch3.6 TOP: Skills Practice 9