Formulas For Areas Of Polygons Coordinate Geometry Formulas

Transcription

Geometry B Exam ReviewThe following formulas will be provided in the examination booklet:Formulas for Areas of PolygonsArea of a Triangle:Area of a Rectangle:Coordinate Geometry FormulasSlope:Distance:Midpoint:Area of a Trapezoid:Right TrianglesArea of a Parallelogram:Area of a Regular Polygon:BcaCAbCircle FormulasArea of a Circle:Circumference of a circle:Arc Length of a Circle:Special Right TrianglesArea of a Sector of a Circle:Area of a Segment of a Circle:Area of sector – Area of triangleoa4530o2aAngle and Arc Formulas:45oa60oaMCPS 2012–20131

Geometry B Exam ReviewThe following formulas will be provided in the examination booklet:Formulas for Volume (V) and Surface Area (SA)Right PrismV Bh area of base heightSA 2 B Ph 2 area of base perimeter height Right Circular CylinderV Bh area of base height r 2 hSA 2 B Ch 2 base circumference height 2 r 2 2 rhRight Pyramid11V Bh area of base height33SA B 11Pl area of base perimeter of base slant height22Right ConeV 111Bh area of base height r 2 h333SA r 2 rlSphere4V r33SA 4 r 2Other FormulasDiagonal of a PrismD L2 W 2 H 2Geometric Mean of Two NumbersMCPS 2012–2013a b2

Geometry B Exam ReviewFor items 1 through 3, determine the area of the following composite figures. If the figureis shaded, find the area of the shaded portion of the figure.Note: Figures NOT drawn to scale1.3. OR and OS are radii2.R16 in12 cm8 ftS20 cm16 in8 ft16 inO16 inFor items 4 and 5, determine the probability that a dart will hit the shaded area of thetarget.Note: Figure NOTdrawn to scale4.3 in6 inA5.14B13C12D347 inNote: Figure NOTdrawn to scale5 in10 in10 inA720MCPS 2012–2013B35C1320D7103

Geometry B Exam Review6.Which of the following statements are true?a.b.7 5 35357 5c.10 3 7d.5 6 11e.32 16 2 4 2For items 7 through 9, determine the distance between the following pairs of points.9. 2 , 6 and 5 ,9 3 , 6 and 2 ,1 1, 1 and 2 ,5 10.Given: Quadrilateral ROTS with vertices as labeled below.7.8.Show that: If the midpoints of the sides of this quadrilateral are connected, thenthe figure formed has opposite sides that are congruent.S(6,6)QR(2,4)MPO(0,0)MCPS 2012–2013NT(8,0)4

Geometry B Exam Review11.Given: Right triangle ABC with coordinates as shown. Point M is themidpoint of BCFind the area of triangle AMBC(0,6)MA(0,0)B(6,0)For items 12 through 14, the lengths of three segments are given. State whether thetriangle formed by the three segments is acute, right, or obtuse. Give reasons for youranswers.12.6, 8, 1013.3, 8, 914.9, 12, 14For items 15 through 23, determine the value of x and/or y in each figure below.Note: Figures NOT drawn to scale15.716.10x4x7417.18.12yxMCPS 2012–201319.31545ox860oxy5

Geometry B Exam Review20.21.30oxxy45o22.23.y30o12xx45o24.A regular hexagon has an area of 96 3 and an apothem of 4 3 . What is thelength of each side of the hexagon?A2B4C8D8 3For items 25 through 31, complete the information for each solid.Note: Figures NOT drawn to scale25.10r 6Surface Area:Volume:A regular hexagon with perimeter 36and area 26.12Surface Area:Volume:MCPS 2012–20136

Geometry B Exam Review27.46BPoint B isat thecenter ofthe squarebase.Slant Height:Surface Area:Volume:6Slant Height:28.Surface Area:4Volume:r 329.Surface Area:4 cmVolume:30.Surface Area:9Volume:105831.6Surface Area:Volume:MCPS 2012–20137

Geometry B Exam Review32.If the radius of a sphere is doubled, what will happen to the surface area of thesphere?ABCD33.If each side of a cube is doubled, what will happen to the volume of the cube?ABCD34.It will increase by a factor of 2.It will increase by a factor of 4.It will increase by a factor of 6.It will increase by a factor of 8.It will increase by a factor of 2.It will increase by a factor of 4.It will increase by a factor of 6.It will increase by a factor of 8.Look at the right rectangular prism below.ECDG7BAa.b.3F5What is the length of segment AE ?What is the relationship between diagonal AE and the prism?35.A cube has a surface area of 24 in2. What is the volume of the cube?36.In the figure below, the two cones are similar:Note: FiguresNOT drawn toscale6154ra. What is the value of r? Explain how you determined your answer.b. What is the ratio of the volumes of the cones? Explain how you determined youranswer.MCPS 2012–20138

Geometry B Exam Review37.If two polygons are similar, what is known about their angles and sides?For items 38 and 39, the polygons are similar. Determine the value of x.x38.39.201521254014xFor items 40 and 41, determine the value of x in each figure below.40.5641.81242.In the figure below, AB // CDEABCNote: Figures NOT drawnto scalex30Note: Figure NOT drawnto scaleDTrue or False?a.b.c.d.e. EAB ECDEA EB EC EDEA EB AC BD EAB is isosceles1AB CD2MCPS 2012–20139

Geometry B Exam Review43.In the figure below, m n p .A23BmCNote: Figure NOTdrawn to scale9DnE86FGpWhat is the perimeter of triangle AFG? Explain how you determined your answer.44.Look at triangles ABC and DCE below.BANote: Figure NOTdrawn to scaleCDEIn parts (a), (b), and (c) below, determine whether the triangles are similar, basedon the given information. Use mathematics to justify your answer.a.AB DEb.BC 14, AC 16DC 21, CE 24c.AB 10, BC 20DE 20, CD 40MCPS 2012–201310

Geometry B Exam Review45.The ratio of the perimeter of two similar polygons is 5:7. What is the ratio of theirareas?46.The ratio of the volumes of two similar solids is 8:27. What is the ratio of theirsurface areas?47.The ratio of the surface areas of two similar solids is 25:36. What is the ratio oftheir volumes?ABCD48.5:625:36125:216625:1296On the coordinate plane below, plot the points A 1, 2 , B 0 ,1 , and C 2 ,3 yxa.b.Show that the triangle is a right triangle and determine its area.Using 0, 0 as the center of dilation and a scale factor of 2, draw thec.dilation image and state the coordinates of each vertex of the image.What is the ratio of the area of the dilation image to the pre-image? Usemathematics to justify your answer.MCPS 2012–201311

Geometry B Exam Review49.Regular pentagon PRSTU below has a perimeter of 60.1It is dilated with a scale factor of , with the center of dilation P, to produce the3shaded pentagon PR S T U .PNote: Figure NOT drawnto scaleURSTWhat is the length of S T ?50.What is the geometric mean of 6 and 12?A2B72 6 2C18D72For items 51 and 52, look at circle P below.A36oNote: Figure NOT drawnBto scaleP20 cm51.AB ?What is the length of A52.4 B8 C80 D160 C40 D160 What is the area of the shaded sector?A4 MCPS 2012–2013B8 12

Geometry B Exam ReviewFor items 53 through 55, find the measure of the angle marked xo53.Note: Figures NOTdrawn to scale54.124xoo55.x2874ooxo56ooo36For items 56 through 58, find the measure of the arc marked xo.56.Note: Figures NOTdrawn to scale57.o26157oo41xoxo58.59oo41MCPS 2012–2013xo13

Geometry B Exam Review59.In circle E below,AB is tangent to the circle at A. 40o , mGH 30om AD 90o mDHA1CB2109834Note: FigureNOT drawn toscaleDEF5G6H7Find the measures of the angles numbered 1–10.Jm 1 m 2 m 3 m 4 m 5 m 6 m 7 m 8 m 9 m 10 60.For a game, a spinner is in the shape of a circle with radius 10 cm. The spinner isdivided into sectors. One sector intercepts an arc of 72 degrees. What is the areaof that sector?For items 61 and 62, find the area of the shaded segments of the circles.61.90oNote: Figure NOTdrawn to scale8 cm120o62.Note: Figure NOTdrawn to scale18 cmMCPS 2012–201314

Geometry B Exam Review63.Note: Figure NOT drawnto scaleCircle O has a diameter of 20.UT 16 , SM 24RS UT , RS SMMLSUOWR64.a.What is the length of OW ?b.What is the length of LM ?TDescribe and sketch the locus of all points in a plane that are equidistant fromeach endpoint of AB .ABFor items 65 and 66, look at the right triangle below.40Note: Figure NOTdrawn to scale94165.Which of the following has a ratio ofA66.sin Bcos Which of the following has a ratio ofAsin MCPS 2012–2013B40?41cos Ctan D None of theseCtan D None of these40?915

Geometry B Exam ReviewFor items 67 through 71, find the value of x.67.68.x124040o70.111769.xo1452ox71.86772.A jet plane begins a steady climb and flies for 3 miles (15840 feet) at an angle of12o with the ground. What was its change in altitude in feet?MCPS 2012–201316

Geometry B Exam Review MCPS 2012-2013 8 32. If the radius of a sphere is doubled, what will happen to the surface area of the sphere?