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Geometry: Chapter QuestionsHow 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?How do you find the volume of a rectangular prism with fractional edge lengths?How do you find the surface area of a 3-dimensional figure using its net?How do you use coordinates to find the length of a side of a polygon?Geometry: Chapter ProblemsRectangles & ParallelogramsClassworkFind the area of each figure.5 ft7 ft12 in3. 15 cm12 cm18 cm16 m13 m7 m29527532385 Do the rectangle and parallelogram below have the same area? Explain why or why not. N 2.5 in 2.5 in. 3 in. 9 in. 9 in.The length of a rectangle is 14.5 in and the width is 3.2 in. What is its area?How do you find the area of a rectangle?How do you find the area of a parallelogram?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 144 cm2?HomeworkFind the area of each figure.8 ft9 ft 14 mm10 cm8 cm15 cm18 m16 m14 m10 cm9 cm17 cmDo the rectangle and parallelogram below have the same area? Explain why or why not. N 4 cm. 6 cm. 4cm. 12 cm. 12 cm.The length of a rectangle is 17 m and the width is 5.25 m. What is its area?How do you find the width of a rectangle when given the length and total area?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 63 cm2?Triangles & TrapezoidsClassworkFind the area of each figure.13 ft7 ft9 ft15 m22 m18 m 12 yd9 yd4 yd18 yd9 yd7 yd10 yd24 yd15 yd8 yd18 yd15 ydThe triangle below has an area of 4.76 sq. in. If the base is 3.4 in., let h be the height in inches. Explain how the equation 4.76 in2= 12(3.4 in.)(h) represents the situation. Solve the equation.6038416138Find the height of a triangle whose area is 40 in2 and whose base is 10 in.Darnell and Donovan are both trying to calculate the area of an obtuse triangle. Examine their calculations below.211836013335Darnell’s WorkDonovan’s WorkA=12×3 in. ×4 in.A=6 in2A=12×12 in. ×4 in.A=24 in2Which student calculated the area correctly? Explain why the other student is not correct.Find the area of the polygons. HomeworkFind the area of each figure.11 ft8 ft9 ft13 m22 m15 m17 yd14 yd9 yd16 yd11 yd9 yd10 yd21 yd12 yd7 yd16 yd12 ydFind the height of a triangle whose area is 50 in2 and whose base is 5 in.Find the base of a triangle whose area is 71.4 m2 and whose height is 8.4 m.xxxx7 cm24 cm25 cm43 cmRussell calculated the area of the triangle below. His work is shown.A=12×43 cm ×7 cmA=150.5 cm2Although 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. Find the area of the polygons. Area of Irregular FiguresClasswork20 in35 in 3 in6 in12 inFind the area of each figure.12 in12 in21 in12 in10 in 3 cm4 cm5 cm19 cm14 cm5 in5 in7 in11 in4 inHomework17 ft18 ft14 ft16 ft16 ft20 ft18 ft15 ftFind the area of each figure.22 cm8 cm11 cm11 cm7 m6 m6 m17 m18 m4 m8 m8 m8 m7 mArea of Shaded Figures12 m 23 m6 m6 mClasswork Find the area of each shaded region.14 m8 m4 m4 m13 m15 m23 m18 m7 mHomework6 cm8 cm4 cm10 cm6 cm4 cm Find the area of each shaded region.32 cm40 cm16 cm24 cm18 cm15 cm7 cm10 cm3 Dimensional Solids & Nets228600090805434340090805Classwork16573540005Name the figure. 228600036576000Give the number faces, edges, and vertices of each shape. Triangular pyramidcube45720000identify the 3-dimensional figure from its net.25146003175022860031750 Draw the net for a rectangular pyramid.Draw the net for a soda can.-5715090805Homework43434006352286000635Name the figure. 3429000-5715276860-64770Give the number faces, edges, and vertices of each shape. square pyramidrectangular prism4572000101600205740010160018097527305Identify the 3-dimensional figure from its net. Draw the net for a 4x4 fence post.Draw the net for a piece of apple pie.Surface AreaClassworkFind the surface area of the figures given their nets.13 in10 in5 m30 m15 m9 m3 m2 m15 yd18 yd15 yd48577568580Draw the net to find the surface area of each figure.20 ft 15 ft9 ft16 ft2857501670059 ft7 ft 7 ftMarley was wrapping a present for her brother’s birthday. The present is 12 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.7 cm11 cm6 cm6 cm 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.HomeworkFind the surface area of the figures given their nets.9 yd9 yd3 yd27 yd9 yd16 in4 in4 in4 in22 yd24 yd20 yd266700179705Draw the net to find the surface area of each figure.3 ft3 ft6 ft8 yd11 yd17 yd15 yd8 in18 in9 in-104775440055 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.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 2 inches. Label the dimensions on the net below and find the total surface area of the box.VolumeClassworkFind the volume of each figure:A 23 m x 16 m x 25 m rectangular prismA cube with edge of 57 ftA box has volume of 24 ft3 and a base of 2 ft by 3 ft, what is its height? cm cm cm The length, width and height of one of the small cubes is 13 m. Find the volume of the figure. The length, width and height of one of the small cubes is 35 cm.Find the volume of the figure. The length, width and height of one of the small cubes is 19 in.Find the volume of the figure. The length, width and height of one of the small cubes is 34 m.Find the volume of the figure.HomeworkFind the volume of each figure:A 45 m x 12 m x 78 m rectangular prismA cube with edges of 49 ftA box has volume of 24 ft3 and a base of 2 ft by 4ft, what is its height? cm cm cm The length, width and height of one of the small cubes is 23 m. Find the volume of the figure. The length, width and height of one of the small cubes is 14 ft.Find the volume of the figure. The length, width and height of one of the small cubes is 15 mm.Find the volume of the figure. The length, width and height of one of the small cubes is 18 m.Find the volume of the figure.Surface Area and Volume Application ProblemsClassworkA 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 17 in by 18 3/4 in by 42 4/5 in. How much space is inside the refrigerator? If a gallon of water is about 215 sq in, approximately how many gallons of water can fit inside this bathtub?This wafer is going to be completely dipped in chocolate. How many square cm need to be covered?HomeworkBlake is donating some outgrown clothes to charity. How many cubic feet of clothes will fit in the box?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?The Johnson family wants to paint their living room. This is a diagram of the room. If one gallon of paint will cover 32 square feet, how many gallons will they need in order to paint their room?A candy company is designing the packaging for its new candy bar. The bars will be packed in cartons which are 1 foot long, 1 foot wide, and 1 foot high. How many of these cartons can they pack into the shipping crate which is 5 ft long, 12 ft wide, and 4 ft high?Polygons in the Coordinate PlaneClassworkPlot the following points and connect them in the order given. Find the distance of each side.A (2.5,2) B (-5 ? 2) C (-5 ?, 5) D (2.5,5)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 (4,-1) S (-1,-1) T (-4,-4) Without plotting the points, find the perimeter of the shape given its coordinates.A (4,-4) B (1,-4) C (1,-1) D (4,-1)Without plotting the points, find the area of the shape given its coordinates.H (-2,-5) I (-2,-2) J (4,-2) K (4,-5)Plot the following points in the order given. What is the name and the area of the shape formed?D (-2,5) E (-5,0.5) F (5,0) G (2,5)Plot the following points in the order given. What is the area of the shape formed?P (-3,1) Q (-5,-4) R (-1,-4)Use the following map to answer the questions below.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.What is the area of the square those locations form?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.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?HomeworkPlot the following points and connect them in the order given. Find the distance of each side.A (2,2.5) B (-3,2?) C (-3,-2) D (2,-2)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 (2,-2) S (-2,-2) T (0,-5) Without plotting the points, find the perimeter of the shape given its coordinates.A (2,-1) B (5,-1) C (5,-5) D (2,-5)Without plotting the points, find the area of the shape given its coordinates.H (1,5) I (1,1) J (-5,1) K (-5,5)Plot the following points in the order given. What is the area of the shape formed?D (1,1) E (4,5) F (-2,5) G (-5,1)Plot the following points in the order given. What is the name and the area of the shape formed?P (-2.5,3) Q (-2,-2) R (4 ? -2)Use the following map to answer the questions below.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 1st quadrant, and forms a right triangle with a base of 4 units and a height of 2 units. What is the location of the Reading? Plot and label it on the map.What is the area of that triangle formed by Cutler, Brookdale and Edison? Fischer Lake Boathouse is 4 units North, and 2 units East of Brookdale. What locations does it form a rectangle with, and what is the perimeter of that rectangle?Geometry Unit Review Multiple Choice QuestionsThe name of the figure made of 6 congruent squares is a:Square PyramidCube241935076200Rectangular PyramidRectangular PrismName the figure represented by this net: Triangular Prism11 cm23 cm9 cm9 cmTriangular PyramidSquare PyramidCylinderWhat is the surface area of the figure associated with this net? 352 cm2451 cm2559 cm2302.5 cm2What is the area of a rectangle with a length of 19 cm and width of 6 cm?114 cm95 cm95 cm2114 cm2A square pyramid has base edges of 8 cm and a height of 15 cm, what is its surface area?120 cm2304 cm2 400 cm2 cm cm cm 244 cm2Find the volume of the figure pictured to the right.124 cm3118 cm21108 cm314 yd12 yd6 yd2216 cm2What is the area of the figure pictured to the right?72 cm298 cm242 cm236 cm2A triangle has an area of 64 yd2 and a base of 8, what is the height of the triangle? 8 yd 24 yd 16 yd 4 yd26 yd14 yd8 yd17 yd14 ydFind the area of the figure to the right.344 cm2172 cm2112 cm2301 cm2Find the height of the figure to the right.A=91cm2? cm13 cm9 cm270 cm594 cm27 cmRachel wants to tile her kitchen floor with tiles that are 1 ft2. If her kitchen is 18 ft by 13 ft, how many tiles will she need?1171,83016 m6 m8 m8 m8 m9 m234468Find the area of the figure to the right.204 m2156 m221 cm19 cm8 cm16 cm120 m2264 m2Find the area of the shaded region to the right. 463 in2271 in2507 in2335 in2A triangle has an area of 48 m2 which combination could be the base and height?12 m; 6 m4 m; 24 m6 m; 8 m12 m; 4 mWhen finding the area of a trapezoid, you first:Multiply the height by 2Find the sum of the two slant heightsFind the sum of the two basesDivide the slant height by 2Find the area of the shape graphed on the right.15 units220 units210 units212 units2Geometry Unit Review Short Constructed Response QuestionsFind the height of a parallelogram with an area of 180 m2 and a base of 15 m. h = _________To create privacy during testing, three windows that each measure 4 m by 2 m needs to be covered. The largest sheets of paper you have measure 2 m by 1.5 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?16 ft8 ft8 ft6 ft9 ft11 ft__________Draw the net of a pentagonal prism.Aiden walked the perimeter of his backyard by walking 16 m north, 13 m west, and arrived back at his starting point. What is the area of Aiden’s backyard?__________Which takes more cardboard to make: 2 boxes of 4x7x6 inches or 1 box of 9x12x11 inches? By how much extra cardboard?____________________In order to decorate for a party, you need to cover 3 rectangular tables with tablecloth. The tables measure 48 in by 60 in. If you want 4 inches overhang on each side, how many square inches of fabric would it take to cover all 3 tables? __________To create privacy in your house, you want to buy drapes to cover your windows. Each set of windows is 72” tall and 60” wide. Each drape is 84” tall and 50” wide. If you have 4 sets of these windows in your house, how many drapes do you need to purchase?Find the volume of the shape below if each small cube has a length, width and height of 12 in.__________Plot the following points in the order given. What is the area of the shape formed?D (2,-2) E (-2,-2) F (-4,-5) G (4,-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 (-2,2) S (-3,4) T (-4,2) __________Without plotting the coordinates, what is the perimeter of the shape formed?H (2,-2) I (-2,-2) J (-2,-5) K (2,-5)Geometry Unit Review Extended Constructed Response QuestionsYour classroom walls are going to be covered with wallpaper. The walls are 120 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? 8 ft4 ft3 ft14 ft25 ft3 ft 5 ft7 ftYour parents have offered to pay you to paint the front of your house with two coats of paint. Paint currently costs $29.97 per gallon and each gallon will cover approximately 350 square feet. Below is a diagram of the front of your house. Calculate how many gallons of paint you need to buy.How much will it cost to complete this job?7 ft7 ft7 ft7 ft7 ft10 ft28 ft46 ftYour 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?7 ft7 ftAn aquarium tank in the shape of a rectangular prism is 8.5 m long, 2 1/4 m wide, and 2 4/5 m high. How much water can the tank hold?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. Calculate how many containers of fertilizer you need.How much will it cost to complete this job?35 ft54 ft7 ft14 ft 7 ft9 ftYour parents offer to pay you $200 to complete the job. How much money will you make if you need to pay for the sod yourself?Plot points A (1, 3) and B (1, 0) and connect them with a line. Plot point C so that you form a scalene right triangle.428625240030What is the ordered pair of point C?Plot points A (-2, 3); B (-3, 1); and C (0, 1) and connect them in the order given. Create and plot point D so that a parallelogram is formed.What is the coordinate of point D?581025233680Name the two sets of parallel sides of the parallelogram. Draw the polygon with the following coordinates: W (-2, -1); X (-2, -4); Y(2, -4); Z (2, -1) and connect them in the order given.Use the coordinates to find the distance of each side of the polygon.What is the perimeter of the shape if each unit represents 1 centimeter?990600180340CW-HW Answer Key35 ft2144 in2 216 cm291 m 280 cm2Yes, 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.46.4 in2A = lwA = bhThe base and the height of a triangle meet to form a right angle.24 cm72 ft2196 mm2120 cm 2224 m2153 cm2No, 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.89.25 m2Divide the total area by the length to get the width.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 cm45.5 ft2 135 m218 yd294.5 yd2168 yd2The equation shows the area, 4.76 in2, is one half the base, 3.4 in., times the height in inches, h.2.8 in = height8 inDonovan 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. 10 sq. units 7 sq. units44 ft297.5 m263 yd2121.5 yd2129.5 yd220 in17 The formula for the area of the a triangle is A=1/2bh. Russell followed this formula because 7 cm is the height of the triangle, and 43 cm is the base of the triangle.6 sq. units 11.5 sq. units388 in2309 in2163.5 cm291 in2516 ft2418 cm2144 m2127 m272 m2168 m2251 m2172cm21088 cm2235 cm2Hexagonal prismCylinderOctagonal prism6 faces, 10 edges, 6 vertices8 faces, 18 edges,12 vertices 4 faces, 6 edges, 4 vertices6 faces, 12 edges, 8 verticesPentagonal pyramidTriangular prismPentagonal pyramid 0207010 Triangular pyramid Pentagonal prismCone4 faces, 6 edges, 4 vertices7 faces, 15 edges, 10 vertices5 faces, 8 edges, 5 vertices6 faces, 16 edges, 8 verticesPentagonal prismSquare pyramidCylinder 429 in2 1350 m2 87 m2517.5 yd2819 ft2 126 ft360 ft2185 cm2486 yd2702 yd2288 in21012 yd2 90 ft2560 yd2558 in2118 in 2245 m3 125343 ft34 ft120 cm3 159 m3 5 23125 cm332729 in35 116 m3 720 m364729 ft3 3 ft 5504 cm3 14 29 m3 38 ft332125 mm3-140970418465 9256 m3 Add the area of each face to find the total surface area. 2(70)+2(140)+2(98)= 616in213,642.5 in3The problem says "approximately" to account for the unavailable space inside the tub. 32x18x59.5=34,272 in265700473645 71.5 cm2 108in3 Add the area of each face to find the total surface area. 2(36) + 4(18)=144 in2 -685800-1143000The sum of the length of each wall times the height: 51+20+23+16.5+28+26.5=162 ft2. Divided by 32 sq ft per gallon = 5+ gallons. So, They will need 6 gallons of paint. Each carton is 1 cubic foot. (12)(5)(4)=240 unit cubes 4572000RUST (1,-4). 12 units18 units2quadrilateral (It does not have a set of parallel sides, so it cannot be a trapezoid.) 21 units2. 10 units2PRQSee map 9 sq unitssee mapAcute, Scalene triangle; A= 22.5 u2see map1/2(3)(5)=7.5 sq unitsSebastian's houseRTUSU (-4,-5) OR (4,-5) 14 units24 units224 units2DEGF obtuse, isosceles triangleSee map see map36 sq unitsisosceles, right trianglesee map(5x8.5)-(6+12.75+6.25)=42.5-25=17.5u2Cutler, Dixon and Reading. P=2(2) + (2)4) = 12 unitsGeometry Unit Review Multiple Choice Question AnswersbccdbcdcbdcbdbccGeometry Unit Review Short Constructed Response Answers12 m8 sheets of paper397 ft2257175-464820104 m2 1 box, 302 in2 more11424 in28 drapes4 in318 units2DGEF3140 mm3(-3,0)RSUT14 unitsGeometry Unit Review Extended Constructed Response Answers1. a. 2(25 x 10) + 2(14x10) - (3x5 + 3x8) = 500 + 280 - 39 = 741 ft2 b. 741 x $0.95 = $703.952. a. (46 x 28) – [(7 x 10) + (7x7)(6)] = 924 ft2 x 2 = 1848 ft2 for two coats, 1848 ÷ 350 = 5.28, 6 gallonsb. 6 x 29.97 = $179.82c. 500 – 179.82 = $320.183. a. 8.5 x 2.25 x 2.8 = 53.55 m3 or 53 11/20 m3b. (8.5 x 2.25) + 2(8.5 x 2.8) + 2(2.25 x 2.8) = 19.125 + 47.6 + 12.6 = 79.325 m2 or 79 13/40m24. a. (54 x 35) – [(14 x 9) + ((7 + 14) x 7) ÷ 2] = 1690.5 ÷ 500 = 3.381, 4 containersb. 4 x 8.75 = $35c. 200 – 35 = $165AB5. Answers may vary [ex: point C could be (5,0), (5,3)]6.D (1,3)BCDThe two sets of parallel sides are AB and DC as well as AD and BC.A7. WX and ZY = 3 centimeters, WZ and XY = 4 centimeters3 + 3 + 4 + 4 = 14 centimetersW25 cmXZY ................
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