Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

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1 Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the area of irregular shapes?. How do you find the area of shaded regions? 5. How do you find the volume of a rectangular prism with fractional edge lengths? 6. How do you find the surface area of a -dimensional figure using its net? 7. How do you use coordinates to find the length of a side of a polygon? NJ Center for Teaching and Learning ~ ~

2 Geometry: Chapter Problems Rectangles & Parallelograms Classwork Find the area of each figure.. 7 ft 5 ft. in.. 5 cm cm. 8 cm 6 m m 7 m Do the rectangle and parallelogram below have the same area? Explain why or why not. N.5 in.5 in. in. 9 in. 9 in. NJ Center for Teaching and Learning ~ ~

3 7. The length of a rectangle is.5 in and the width is. in. What is its area? 8. How do you find the area of a rectangle? 9. How do you find the area of a parallelogram? 0. What is true of the base and height of a parallelogram?. What is the base of a parallelogram whose height is 6 cm and whose area is cm? Homework Find the area of each figure.. 9 ft 8 ft. mm. 0 cm 8 cm 5 cm 5. 8 m 6 m m 6. 0 cm 9 cm 7 cm NJ Center for Teaching and Learning ~ ~

4 7. Do the rectangle and parallelogram below have the same area? Explain why or why not. N cm. 6 cm. cm. cm. cm. 8. The length of a rectangle is 7 m and the width is 5.5 m. What is its area? 9. How do you find the width of a rectangle when given the length and total area? 0. How do you find the base of a parallelogram when given the height and total area?. What is true of the base and height of a parallelogram?. What is the base of a parallelogram whose height is 7 cm and whose area is 6 cm? Triangles & Trapezoids Classwork Find the area of each figure.. 7 ft 9 ft ft. 8 m m 5 m 5. yd 9 yd yd NJ Center for Teaching and Learning ~ ~

5 6. 8 yd 7 yd 0 yd 9 yd 7. 8 yd 5 yd 8 yd 5 yd yd 8. The triangle below has an area of.76 sq. in. If the base is. in., let h be the height in inches. Explain how the equation.76 in = (. in. )(h) represents the situation. Solve the equation. 9. Find the height of a triangle whose area is 0 in and whose base is 0 in. 0. Darnell and Donovan are both trying to calculate the area of an obtuse triangle. Examine their calculations below. Darnell s Work A = in. in. A = 6 in Donovan s Work A = in. in. A = in Which student calculated the area correctly? Explain why the other student is not correct. From engage ny From engage ny NJ Center for Teaching and Learning ~ 5 ~

6 Find the area of the polygons... Homework Find the area of each figure.. 8 ft 9 ft ft. 5 m m 5. 7 yd m yd 9 yd NJ Center for Teaching and Learning ~ 6 ~

7 6. 6 yd 9 yd 0 yd yd 7. yd 7 yd 6 yd yd yd 8. Find the height of a triangle whose area is 50 in and whose base is 5 in. 9. Find the base of a triangle whose area is 7. m and whose height is 8. m. 0. Russell calculated the area of the triangle below. His work is shown. 5 cm cm 5 cm x 7 cm cm A = cm 7 cm A = 50.5 cm Although Russell was told his work is correct, he had a hard time explaining why it is correct. Help Russell explain why is calculations are correct. From engage ny NJ Center for Teaching and Learning ~ 7 ~

8 Find the area of the polygons... Area of Irregular Figures Classwork Find the area of each figure.. 6 in in in 0 in 5 in. in in in 0 in in NJ Center for Teaching and Learning ~ 8 ~

9 5. cm cm cm 5 cm 9 cm 6. 5 in 5 in in in 7 in Homework Find the area of each figure ft 6 ft 5 ft 8 ft 0 ft 7 ft 8 ft 8. cm ft cm 8 cm cm NJ Center for Teaching and Learning ~ 9 ~

10 9. 6 m 7 m 6 m 7 m 50. m 8 m 8 m 7 m 8 m 8 m Area of Shaded Figures Classwork Find the area of each shaded region. 5. m m 5. 6 m 6 m m m 8 m m NJ Center for Teaching and Learning ~ 0 ~

11 m 5. 8 m 7 m m Homework Find the area of each shaded region cm 5 m cm 6 cm 6 cm 8 cm 55. cm 6 cm cm cm 0 cm cm 5 cm 7 cm 8 cm NJ Center for Teaching and Learning ~ ~

12 Dimensional Solids & Nets Classwork Name the figure Give the number faces, edges, and vertices of each shape Triangular pyramid 6. cube identify the -dimensional figure from its net Draw the net for a rectangular pyramid. 68. Draw the net for a soda can. Homework Name the figure NJ Center for Teaching and Learning ~ ~

13 Give the number faces, edges, and vertices of each shape square pyramid 75. rectangular prism Identify the -dimensional figure from its net Draw the net for a x fence post. 80. Draw the net for a piece of apple pie. Surface Area Classwork Find the surface area of the figures given their nets in in NJ Center for Teaching and Learning ~ ~

14 8. 5 m 5 m 0 m 8. m 9 m m 8. 8 yd 5 yd 5 yd Draw the net to find the surface area of each figure ft 6 ft 0 ft 5 ft ft 9 ft 7 ft NJ Center for Teaching and Learning ~ ~

15 87. Marley was wrapping a present for her brother s birthday. The present is inches long, 6 inches wide, and 6 inches tall. Label the net below to find the surface area of the present and determine at least how many square inches of wrapping paper she needs to use. 88. Joseph wants to paint the surface of a wooden pyramid he built. Use the net below to calculate how many square centimeters of paint Joseph will need to buy in order to paint his pyramid. 6 cm 6 cm cm 7 cm Homework Find the surface area of the figures given their nets yd 9 yd NJ Center for Teaching and Learning ~ 5 ~

16 90. yd 9 yd 6 in 7 yd 9. in in in 9. yd 0 yd yd Draw the net to find the surface area of each figure ft ft ft NJ Center for Teaching and Learning ~ 6 ~

17 9. 5 yd 8 yd yd 7 yd 95. A cookie company designed a new box for their chocolate chip cookies. Using the net below, find the surface area of the new box so the company knows how many square inches of cardboard are required for each package. 8 in 8 in 9 in 96. The net below represents a box created to ship clothing. The box below has a length of 7 in, a width of 5 in, and a height of inches. Label the dimensions on the net below and find the total surface area of the box. Volume Classwork Find the volume of each figure: 97. A m x m x m rectangular prism A cube with edge of 5 7 ft 99. A box has volume of ft and a base of ft by ft, what is its height? NJ Center for Teaching and Learning ~ 7 ~

18 00. cm cm cm 0. The length, width and height of one of the small cubes is m. Find the volume of the figure. 0. The length, width and height of one of the small cubes is 5 cm. Find the volume of the figure. 0. The length, width and height of one of the small cubes is 9 in. Find the volume of the figure. 0. The length, width and height of one of the small cubes is m. Find the volume of the figure. NJ Center for Teaching and Learning ~ 8 ~

19 Homework Find the volume of each figure: 05. A m x m x 7 m rectangular prism A cube with edges of 9 ft 07. A box has volume of ft and a base of ft by ft, what is its height? 08. cm cm cm 09. The length, width and height of one of the small cubes is m. Find the volume of the figure. 0. The length, width and height of one of the small cubes is ft. Find the volume of the figure.. The length, width and height of one of the small cubes is 5 mm. Find the volume of the figure. NJ Center for Teaching and Learning ~ 9 ~

20 . The length, width and height of one of the small cubes is 8 m. Find the volume of the figure. Surface Area and Volume Application Problems Classwork. A birthday gift is placed inside the box shown. Draw and label a net for this box, and show how you can use the net to determine the minimum amount of wrapping paper needed to wrap this gift?. The inside of a refrigerator in a medical laboratory measures 7 in by 8 / in by /5 in. How much space is inside the refrigerator? 5. If a gallon of water is about 5 sq in, approximately how many gallons of water can fit inside this bathtub? 6. This wafer is going to be completely dipped in chocolate. How many square cm need to be covered? NJ Center for Teaching and Learning ~ 0 ~

21 Homework 7. Blake is donating some outgrown clothes to charity. How many cubic feet of clothes will fit in the box? 8. Blake must wrap the box in packaging paper. Draw and label a net for this box, and show how you can use the net to determine the minimum amount of packaging paper needed to wrap this box? 9. The Johnson family wants to paint their living room. This is a diagram of the room. If one gallon of paint will cover square feet, how many gallons will they need in order to paint their room? 0. A candy company is designing the packaging for its new candy bar. The bars will be packed in cartons which are foot long, foot wide, and foot high. How many of these cartons can they pack into the shipping crate which is 5 ft long, ft wide, and ft high? NJ Center for Teaching and Learning ~ ~

22 Polygons in the Coordinate Plane Classwork. Plot the following points and connect them in the order given. Find the distance of each side. A (.5,) B (-5 ½ ) C (-5 ½, 5) D (.5,5) Plot the following points and connect them in the order given. What would be the coordinate of a fourth point that would form a parallelogram? R (,-) S (-,-) T (,) Without plotting the points, find the perimeter of the shape given its coordinates. A (,) B (,) C (,-) D (,-). Without plotting the points, find the area of the shape given its coordinates. H (-,-5) I (-,-) J (,-) K (,-5) 5. Plot the following points in the order given. What is the name and the area of the shape formed? D (-,5) E (-5,0.5) F (5,0) G (,5) NJ Center for Teaching and Learning ~ ~

23 6. Plot the following points in the order given. What is the area of the shape formed? P (-,) Q (-5,) R (-,) Use the following map to answer the questions below. 7. The town library forms a square with Sebastian s house, Ulysses house and Rodger s house. What is the location of the town library? Plot and label it on the map. 8. What is the area of the square those locations form? 9. The grocery store forms a parallelogram with Tara s house, Quincy s house, and Sebastian s house. What is the location of the grocery store? Plot and label it on the map. 0. What polygon does Sebastian s house, Quincy s house and the town library form? Be as specific as possible. The, give the area that this shape covers.. The schoolhouse is in the third quadrant, and forms a right, scalene triangle with Ulysses house and the grocery store. What is the location of the schoolhouse? Plot and label it on the map.. What is the area of that triangle?. The town library, the grocery store and the schoolhouse form a trapezoid with which location? NJ Center for Teaching and Learning ~ ~

24 Homework. Plot the following points and connect them in the order given. Find the distance of each side. A (,.5) B (-,½) C (-,-) D (,-) Plot the following points and connect them in the order given. What would be the coordinate of a fourth point that would form a parallelogram? R (,-) S (-,-) T (0,-5) Without plotting the points, find the perimeter of the shape given its coordinates. A (,-) B (5,-) C (5,-5) D (,-5) 7. Without plotting the points, find the area of the shape given its coordinates. H (,5) I (,) J (-5,) K (-5,5) 8. Plot the following points in the order given. What is the area of the shape formed? D (,) E (,5) F (-,5) G (-5,) NJ Center for Teaching and Learning ~ ~

25 9. Plot the following points in the order given. What is the name and the area of the shape formed? P (-.5,) Q (-,-) R ( ½ -) Use the following map to answer the questions below. 0. Flemington forms a trapezoid with Cutler, Dixon and Brookdale. What is the location of the town Flemington? Plot and label it on the map.. Brookdale, Dixon and Flemington, and Rockaway form a square. What is the location of the Rockaway? Plot and label it on the map.. What is the area of the square formed by those locations?. What polygon does Dixon, Brookdale and Flemington form? Be as specific as possible.. Reading lies in the st quadrant, and forms a right triangle with a base of units and a height of units. What is the location of the Reading? Plot and label it on the map. 5. What is the area of that triangle formed by Cutler, Brookdale and Edison? 6. Fischer Lake Boathouse is units North, and units East of Brookdale. What locations does it form a rectangle with, and what is the perimeter of that rectangle? NJ Center for Teaching and Learning ~ 5 ~

26 Geometry Unit Review Multiple Choice Questions. The name of the figure made of 6 congruent squares is a: a. Square Pyramid b. Cube c. Rectangular Pyramid d. Rectangular Prism. Name the figure represented by this net: a. Triangular Prism b. Triangular Pyramid c. Square Pyramid d. Cylinder. What is the surface area of the figure associated with this net? a. 5 cm b. 5 cm c. 559 cm d. 0.5 cm 9 cm cm cm 9 cm. What is the area of a rectangle with a length of 9 cm and width of 6 cm? a. cm b. 95 cm c. 95 cm d. cm 5. A square pyramid has base edges of 8 cm and a height of 5 cm, what is its surface area? a. 0 cm b. 0 cm c. 00 cm d. cm 6. Find the volume of the figure pictured to the right. a. b. c. d. cm 8 cm 08 cm 6 cm 7. What is the area of the figure pictured to the right? a. 7 cm b. 98 cm c. cm d. 6 cm 8. A triangle has an area of 6 yd and a base of 8, what is the height of the triangle? a. 8 yd b. yd c. 6 yd d. yd cm yd 6 yd cm cm yd NJ Center for Teaching and Learning ~ 6 ~

27 9. Find the area of the figure to the right. a. cm b. 7 cm c. cm d. 0 cm yd 0. Find the height of the figure to the right. a. 9 cm b. 70 cm c. 59 cm d. 7 cm 8 yd A=9cm 7 yd 6 yd? cm cm yd. Rachel wants to tile her kitchen floor with tiles that are ft. If her kitchen is 8 ft by ft, how many tiles will she need? a. 7 b.,80 c. d m. Find the area of the figure to the right. a. 0 m b. 56 m c. 0 m d. 6 m. Find the area of the shaded region to the right. a. 6 in b. 7 in c. 507 in d. 5 in 6 m 8 m 9 m 8 m 8 m 6 cm cm 8 cm. A triangle has an area of 8 m which combination could be the base and height? a. m; 6 m b. m; m c. 6 m; 8 m d. m; m 9 cm 5. When finding the area of a trapezoid, you first: a. Multiply the height by b. Find the sum of the two slant heights c. Find the sum of the two bases d. Divide the slant height by 6. Find the area of the shape graphed on the right. a. 5 units b. 0 units c. 0 units d. units NJ Center for Teaching and Learning ~ 7 ~

28 Geometry Unit Review Short Constructed Response Questions. Find the height of a parallelogram with an area of 80 m and a base of 5 m. h =. To create privacy during testing, three windows that each measure m by m needs to be covered. The largest sheets of paper you have measure m by.5 m. How many sheets of paper will it take to cover the window?. A diagram of a math classroom is below. How much carpet is needed to re-carpet the shaded portion of the floor? 6 ft 8 ft 8 ft ft 6 ft 9 ft. Draw the net of a pentagonal prism. 5. Aiden walked the perimeter of his backyard by walking 6 m north, m west, and arrived back at his starting point. What is the area of Aiden s backyard? 6. Which takes more cardboard to make: boxes of x7x6 inches or box of 9xx inches? By how much extra cardboard? 7. In order to decorate for a party, you need to cover rectangular tables with tablecloth. The tables measure 8 in by 60 in. If you want inches overhang on each side, how many square inches of fabric would it take to cover all tables? 8. To create privacy in your house, you want to buy drapes to cover your windows. Each set of windows is 7 tall and 60 wide. Each drape is 8 tall and 50 wide. If you have sets of these windows in your house, how many drapes do you need to purchase? NJ Center for Teaching and Learning ~ 8 ~

29 9. Find the volume of the shape below if each small cube has a length, width and height of in. 0. Plot the following points in the order given. What is the area of the shape formed? D (,-) E (-,-) F (,-5) G (,-5) Find the volume of the shape below. mm mm mm. Plot the following points and connect them in the order given. What would be the coordinate of a fourth point that would form a rhombus? R (-,) S (-,) T (,) NJ Center for Teaching and Learning ~ 9 ~

30 . Without plotting the coordinates, what is the perimeter of the shape formed? H (,-) I (-,-) J (-,-5) K (,-5) Geometry Unit Review Extended Constructed Response Questions. Your classroom walls are going to be covered with wallpaper. The walls are 0 inches high. The wallpaper costs $0.95 per square foot. Below is a diagram of the classroom. The white boxes represent windows. a. Calculate how many square feet of wallpaper you will need for the classroom. b. How much will it cost to complete this job? 5 ft ft 8 ft ft 5 ft 7 ft ft ft NJ Center for Teaching and Learning ~ 0 ~

31 . Your parents have offered to pay you to paint the front of your house with two coats of paint. Paint currently costs $9.97 per gallon and each gallon will cover approximately 50 square feet. Below is a diagram of the front of your house. a. Calculate how many gallons of paint you need to buy. b. How much will it cost to complete this job? c. Your parents offer to pay you $500 to complete the job. How much money will you make if you need to pay for the paint yourself? 6 ft 7 ft 7 ft 7 ft 7 ft 7 ft 7 ft 7 ft 8 ft 0 ft. An aquarium tank in the shape of a rectangular prism is 8.5 m long, / m wide, and /5 m high. a. How much water can the tank hold? b. If the top of the tank is open, how much tinting is needed to cover the glass on the tank?. Your parents have offered to pay you to fertilize your backyard. Fertilizer currently costs $8.75 for per container and will cover 500 square feet. Below is a diagram of your backyard. a. Calculate how many containers of fertilizer you need. b. How much will it cost to complete this job? c. Your parents offer to pay you $00 to complete the job. How much money will you make if you need to pay for the sod yourself? 5 ft 7 ft 5 ft 7 ft ft 9 ft NJ Center for Teaching and Learning ~ ~

32 5. Plot points A (, ) and B (, 0) and connect them with a line. a. Plot point C so that you form a scalene right triangle. b. What is the ordered pair of point C? Plot points A (-, ); B (-, ); and C (0, ) and connect them in the order given. Create and plot point D so that a parallelogram is formed. a. What is the coordinate of point D? b. Name the two sets of parallel sides of the parallelogram NJ Center for Teaching and Learning ~ ~

33 7. Draw the polygon with the following coordinates: W (-, -); X (-, ); Y(, ); Z (, -) and connect them in the order given. a. Use the coordinates to find the distance of each side of the polygon. b. What is the perimeter of the shape if each unit represents centimeter? NJ Center for Teaching and Learning ~ ~

34 CW-HW Answer Key. 5 ft. in. 6 cm. 9 m cm 6. Yes, the rectangle and parallelogram have the same area because if we cut off the triangle on the right side of the parallelogram, we can move it over to the left and make the parallelogram into a rectangle. Then they would have the same dimensions so their areas would be the same in 8. A = lw 9. A = bh 0. The base and the height of a triangle meet to form a right angle.. cm. 7 ft. 96 mm. 0 cm 5. m 6. 5 cm 7. No, the rectangle and parallelogram do not have the same height, so even though they have the same length, they do not have the same area m 9. Divide the total area by the length to get the width. 0. Divide the total area by the height to get the base.. The base and the height of a triangle meet to form a right angle.. 9 cm. 5.5 ft. 5 m 5. 8 yd yd yd 8. The equation shows the area,.76 in, is one half the base,. in., times the height in inches, h..8 in = height 9. 8 in 0. Donovan calculated the area correctly. Although Darnell did use the altitude of the triangle, he used the length between the altitude and the base, rather than the actual base.. 0 sq. units. 7 sq. units. ft m 5. 6 yd 6..5 yd yd 8. 0 in The formula for the area of the a triangle is A=/bh. Russell followed this formula because 7 cm is the height of the triangle, and cm is the base of the triangle.. 6 sq. units..5 sq. units. 88 in. 09 in cm 6. 9 in ft 8. 8 cm 9. m m 5. 7 m m 5. 5 m 5. 7cm cm cm 57. Hexagonal prism 58. Cylinder 59. Octagonal prism faces, 0 edges, 6 vertices 6. 8 faces, 8 edges, vertices 6. faces, 6 edges, vertices 6. 6 faces, edges, 8 vertices 6. Pentagonal pyramid 65. Triangular prism 66. Pentagonal pyramid Triangular pyramid 70. Pentagonal prism 7. Cone 7. faces, 6 edges, vertices 7. 7 faces, 5 edges, 0 vertices 7. 5 faces, 8 edges, 5 vertices faces, 6 edges, 8 vertices NJ Center for Teaching and Learning ~ ~

35 76. Pentagonal prism 77. Square pyramid 78. Cylinder in m m yd ft ft ft cm yd yd in 9. 0 yd ft yd in in m ft 99. ft cm m cm in m m ft 07. ft cm m 0. 8 ft. 5 mm m. Add the area of each face to find the total surface area. (70)+(0)+(98)= 66in.,6.5 in 5. The problem says "approximately" to account for the unavailable space inside the tub. x8x59.5=,7 in cm 7. 08in 8. Add the area of each face to find the total surface area. (6) + (8)= in NJ Center for Teaching and Learning ~ 5 ~

36 9. The sum of the length of each wall times the height: =6 ft. Divided by sq ft per gallon = 5+ gallons. So, They will need 6 gallons of paint. 0. Each carton is cubic foot. ()(5)()=0 unit cubes.. (,) S R T - U.. units. 8 units 5. quadrilateral (It does not have a set of parallel sides, so it cannot be a trapezoid.) units NJ Center for Teaching and Learning ~ 6 ~

37 6.. 0 units P Q - R 7. See map 8. 9 sq units 9. see map 0. Acute, Scalene triangle; A=.5 u. see map. /()(5)=7.5 sq units. Sebastian's house. 5. (,-5) OR (,-5) S R U T U NJ Center for Teaching and Learning ~ 7 ~

38 6. units 7. units 8. units F E G D obtuse, isosceles triangle 0. See map. see map. 6 sq units. isosceles, right triangle. see map 5. (5x8.5)-( )=.5-5=7.5u 6. Cutler, Dixon and Reading. P=() + ()) = units NJ Center for Teaching and Learning ~ 8 ~

39 Geometry Unit Review Multiple Choice Question Answers. b. c. c. d 5. b 6. c 7. d 8. c 9. b 0. d. c. b. d. b 5. c 6. c Geometry Unit Review Short Constructed Response Answers. m. 8 sheets of paper. 97 ft m 6. box, 0 in more 7. in 8. 8 drapes 9. in 0. 8 units E D F G. 0 mm. (-,0) T U S R units NJ Center for Teaching and Learning ~ 9 ~

40 Geometry Unit Review Extended Constructed Response Answers.... a. (5 x 0) + (x0) - (x5 + x8) = = 7 ft b. 7 x $0.95 = $70.95 a. (6 x 8) [(7 x 0) + (7x7)(6)] = 9 ft x = 88 ft for two coats, = 5.8, 6 gallons b. 6 x 9.97 = $79.8 c = $0.8 a. 8.5 x.5 x.8 = 5.55 m or 5 /0 m b. (8.5 x.5) + (8.5 x.8) + (.5 x.8) = = 79.5 m or 79 /0m a. (5 x 5) [( x 9) + ((7 + ) x 7) ] = =.8, containers b. x 8.75 = $5 c = $65 5. Answers may vary [ex: point C could be (5,0), (5,)] A B a. D (,) b. The two sets of parallel sides are AB and DC as well as AD and BC. A D B C NJ Center for Teaching and Learning ~ 0 ~

41 7. a. WX and ZY = centimeters, WZ and XY = centimeters b = centimeters W - Z - X - Y NJ Center for Teaching and Learning ~ ~