Acc.Geo
Name:
Semester2
ProblemSet#7–SurfaceAreaandVolume
Surfaceareaandvolumeisatopicwhereformulasarederivedinclass,butmostofthework,
assignmentsandprojectsarecompletedoutsideofclass.Useyourproblemsetsforpracticeand
understandingoftheuseoftheformulasrelatedtoeachfigure.Therefore,foreachproblemthatthat
lendsitselftoadiagram,(1)drawoneorusetheonegiven.(2)Analyzethediagrambymarkinggiven
information.(3)Writeeveryformulausedtosolvetheproblem.Andasalways,(4)SHOWALLWORK.
ANSWERSALONEWILLNOTRECEIVECREDIT.(5)Answersmustbeexact,unlessotherwisenoted.
1. Theareaofanoriginaltriangleis240.Findtheareaofthetriangleformedbyjoining
consecutivemidpointsofthetriangle.
2. Findtheapothemtheregularhexagonshownifthesidelengthsare12.
3. Inanequiangularpolygon,thedegreemeasureofeachexteriorangleofthepolygonis20%of
thedegreemeasureofeachinteriorangleofthepolygon.Findthenumberofsidesofthe
polygon.
4. Findtheareaofthefollowingtrapezoidbelow:
5. Theperimeteroftheparallelogramis154;findit’sarea.
6. Findtheareaofthefollowingtrapezoid.
7. Forthetrianglesasshown,findtheareaof∆DEF.
8. Findthetotalsurfaceareofthefiguretotheright.Thetriangleandthetrapezoidareisosceles,
witheachregionhavingthesameheight.
9. Theradiusofawheelis3.5centimeters.Tothenearestwholenumber,howmanyrevolutions
diditmakeifitisrolledadistanceof 500 ?
10. Ifthebaseis25%oftheheight,findtheareaofthetriangleformedbytheintersectionofthe
diagonalsoftherectangle,oneoftheverticesoftherectangle,andthemidpointofthebaseof
therectangle.
8-2x
x+6
11. Oneangleofatriangleistwiceanother.Thethirdangleexceedsfourtimesthesmallerby12
degrees.Findtheareaofthetriangleifthebaseoppositethelargestangleis24units.Give
answertothenearesthundredth.
12. Findtheareaoftheshadedregion.Assumeregularpolygons.
13. Ifthevolumeofasphereis635cm3,finditssurfaceareatothenearesttenth.
14. Findthetotalsurfaceareaofthefigureshown.
15. Onediagonalofarhombushasalengthof900andaperimeterof2120.Findthelengthofthe
otherdiagonal.
16. Thespanofaregularhexagonis40.Findthehexagon’sarea.
3
4
17. Alinehasanx‐interceptof3aanday‐interceptof4b.Theslopeofthelineis  andb=ka.
Whatisthevalueofk?
18. ABCisarighttrianglewithrightC.IfCD=12andAD=9,findCB.Leaveanswerinsimplified
radicalform.
C
A
D
B
19. Aparallelogramhasdiagonalsof32unitsand44units.Findtheperimeteriftheparallelogramif
oneofthesidesmeasures26units.
20. Fromasquarepieceofpaper,isoscelestrianglesarecutoffofeachcornersothatthata
rectangleremainsasshowninthediagram.Thetotalareaofthetrianglesthatwerecutoffis
100cm2.Whatisthelengthofthediagonaloftherectangle?
21. Twosidesofatriangleare17and16,andthealtitudetothethirdsideis15.Findthethirdside.
22. Findthemeasureofx.
85
A x
65
23. Findthesurfaceareaofthefigureshown.
24. Findtheareaoftheshadedregion.
25. Findthetotalsurfaceareaofthefigureshown.
26. Findthetotalsurfaceareaofthesolidfiguregeneratedbyrotatingitabouttheaxisshown.
27. Findthesurfaceareaofaregularhexahedronwithanedgemeasuring11 3 cm.
28. Findthevolumeofthefollowingfigure.
29. Fivecongruentcirclesaretangenttoeachotherasshowninthediagram.Asquareisformedby
connectingthecentersof4ofthecircles.Whatistheratiooftheshadedareatotheunshaded
areaofthesquare?
30. FindthecoordinatesofBsothat∆ABDwillhavethesameareaas∆ACD.