StudyGuideAnswerKEY
ComplexPolygonsandCircles–AreasandCircumference
1)Findtheareaofthecomplexshape.
3in
5in
3in
9in
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AreaofTriangle= ! b=9–5=4
h=3
AreaofTriangle=4(3)/2
=6𝒊𝒏𝟐 AreaofRectangle=bh
=9(3)
=27𝒊𝒏𝟐 TotalAREA=6+27=33𝒊𝒏𝟐 2)Findtheareaoftheshadedregion.
11m
5m
6m
13m
heightoftrapezoid=15m.
AreaofTrapezoid=
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=180𝒎𝟐 Areaoftherectangle=bh
=6(5)
=30𝒎𝟐 Areaoftheshadedregion=AreaofTrapezoid–AreaofRectangle
=180𝑚! -30𝑚! =150𝒎𝟐 3)Findthecircumferenceandareaofacirclethathasaradiusof6cm.
r=6cm
d=6(2)=12cm
C=𝜋𝑑
A=𝜋𝑟 ! C=3.14(12) A=3.14(6! )
C=37.68cm A=3.14(36) A=113.04𝒄𝒎𝟐 Answerin𝝅 Answerin𝝅 C=12𝝅
A=36𝝅
4)Ifacirclehasanareaof70𝒊𝒏𝟐 ,whatisthediameter?
𝐴 = 𝜋𝑟 ! FORMULA
70=3.14𝑟 ! Pluginwhatyoudoknow.
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Dividebothsidesby3.14.
22.29=𝑟 ! Squarerootbothsides.****𝑟 ! =r(r)
22.29 = 𝑟 ! 4.72in=r
diameter=radiusx2
d=4.72(2)
d=9.44in
5)
7ft
A=Areaofasemicircle+Areaofarectangle
8ft
Areaofthecircle=𝜋𝑟 ! Areaofthesemicircle=
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Diameter=7ft
Radius=7/2=3.5ft
Areaofsemicircle=
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=19.23𝒇𝒕𝟐 Areaoftherectangle=bh
=(8)(7)
=56𝒇𝒕𝟐 TotalAREA=19.23𝒇𝒕𝟐 +56𝒇𝒕𝟐 =75.23𝒇𝒕𝟐