Geometry Chapter 8: Area Review PA Anchors: A3; B2; Cl 1. Find the missing value given BCDA is a rectangle.
Perimeter = 62 cm
Area =
A =- !uJ V:. d.t-\" ~vJ
?
B .---_ _ _ _---,c
A
~ J. ':. .1 i+ ';).LI1)
~). -::
~
rJ
U1l)
-~-J -:..
-;:
(\Y.CW\L llL~ ")
0' ~3~
.1.t+~4 - '0 ....,
17 em
'",0
G)..L
""T
,<+. ... Sl­
2. Find the missing value given BCDA is a rectangle.
Perimeter = 56 cm
Area = ? B
A -- ( t ? CW>k
~ ' -:. ;,l.Q.. + :J.(3 )
C
_).{,
13 em
.J... It; ~
~
V
I3~ )
6 -:. Iqs- ~VYI"9
'5(, .~ J. J..-4- :U.,11
A
p.. ,:- L..u
J":..2.l.. -+-Jw
"U
::. ~
;J
IS"':. . ..J­
3. Calculate the area of the figure.
A=- A(~)'" ~
m_ _,>""",,,,<..,,"-,-,R
Q..,-_4='-='-""-,--7_c-r
~
:l.:Q
L
,'3"",
\
6cm
,
3clrJ'\
'T
~
p
u
...
3 cm
r­
A :..
A -:-. .
S
!w-l-~
'4
t
l?'\
Jl. L> Gl">'\ ) -+ l? L---. )[ ~ (A"n
}. :: 'J,.U: ~4-
q ~L
(£??0 )
4. Calculate the area of the figure.
A; ACD~
Q
lD
A-;: L.u -
4km
1.t.J
To)
).. '# (\Y ~l.\?.\:-w-) - (Yt.n..ll4,~..,... ')
u
A-;
12 km
Hib L-n-t. - Ito ¥-mt,...­
CF'
7- \
P
A~
'? J...
kl?'\l..)
W
14 km
5. Calculate the area of the figure.
Q
R
L
.-J \9
l\ -:. &-l..u.J
_A ~ l'(;~l(J \' f'Y\) -U37,...,...1 ~ rn
5m
T~
15 m
I
'S
i
A ::: =>.\}O
i
,V
U
L
p
h
I
16m
)
m2.._ 2.Y rY)L
~1S-~0
w
6. Calculate the area of the figure.
Q
~
c,
7 mm
,
d)
R
'<h",
~
\
L
I jI.. ....'X
2mm
I
\
4mm
T
~~"1
02".""
-l
p
'7t'>'\.. M
I
u
I
S
A :: J-\p T~
A : . w -+ j...uJ
A:: l,?WI.-n'.( 4 m ........ ) 4- ~nw~-~m.YV\)
~ :::. ;).I) )~ M ~'7"
4 .........~
(074"'0
7. Find the area of parallelogram .MNOP.
P
0
A/b~1
o
A =-- (l . ~ C VY'I ) ( 'i .S-~ )
4.5 em
,.~
Cftl')
'--____--'- ___ .r::
M
1.6 em
N
8. Find the area of parallelogram .A1NOP.
P
0
A~bh
.A -:=:-( \ ,1 (.¥'Y\ X4 f6 (~ ')
0~ · I("u0 4.8 em
~ _ _ _- L
M
1.7 em
___
.r::
N
9. Find the area of parallelogram QRST.
s
A ~-
bh
A -;. (LP<t rr.Y: 5'4 m)
cJ!3,ln-;.
0
10. Find the area of parallelogram QRST.
R____
57_i_ll_---;;s
A ::.- b~
A -==-( 5 -=t Q~_----L..-'--_----/
Cf-:. ::/,
I
I')
Y'4 "4 ~
l. -=1'1
,»
Y") )
A-;. hbh
11. Find the area of MBC.
A~ ~
B
~
~~ \44 ~d~)
9 yd:
A
-E
>
32 yd
(3:1 ~~:iq ~J.)
C
12. Find the area of MBC.
B
~
16 ft
:
6 ft
4ft!
A
<
c
CE~
>
20 ft
13 . Find the area of trapezoid ABCD.
A ~ k lb .+b.l-) h
C
~
A -,. ~(;toP,,-X4f'..)
A ~ ~ (;24 + ??-"X.. I \)
p.. -;. :r 5~ ' II
,A ~ 30).-; ml-
D
14. Find the area oftrapezoidABCD.
16m
B
12
m
:' 11 m
(
:-J
C
~D
A
30 m
.A:: ~(b.-rb-,,",)n A ~ J,.,. (\<O+"30~11 )
A -:; ~ ('..H ..;)li \)
0 -:
:253
()')1....)
15. Find the area of kite RSTU.
s
R~__==~
u
.A ~
__~=-__~T
A-;
<2 ~
kd.cl2­
~ (:l;)"t'\)(~;¥)")
4*,0
'fD
R.~
16. Find the area of kite RSTU.
.A ~ 5:. dl t~2.
~ -;.. ~ (.t3 I ,<'J...<t. ', ~)
0~q~;n9
s
R
T
u
17. A rectangular piece of fabric measures 37 by 36 inches. A triangular scarf with a height of
31 inches and a base of 28 inches is cut from the fabric. How much fabric is left over?
.,A -- k
-A~
.A ~ Lw - ~bh
A -.. (,1 , ..,'[3(q; ,.,) - ~ (~ .\~"t3 I. ,. ')
A-: lJ?>3~
~7"~
'I(\~-
'+3/f-;..,'"'
ii\0
18. A rectangular piece of fabric measures 45 by 37 inches. A triangular scarf with a height of
29 inches and a base of 32 inches is cut from the fabric. How much fabric is left over?
A:: Aa-At'I.
A -;.. .t<..t.) - -5 bh
A . . . (45; ;/,\'/..37 ;0) <~ (3l "" j:.?-t:t ",")
A
~ II (,,~~-
\ )'l'l- -
4(...~ In1­
G I,OLO'9
19. Find the area of the regular polygon.
A > ~at:>n
/A-;-
:i-( 5~ r,'f L, i ,,:'i. k ")
>-~
I
(£"Q3. (., ;"
6 in.
20. Find the area of the regular polygon.
.
.A) ~a.s.V)
S
A > ~(SIS- ',f))L~,~'is')
T
~~ lt~ \ n~ 8 in.
21. If a regular octagon with 2-centimeter sides has an approximate area of
19 centimeters squared, what is the approximate length of the apothem, to the nearest
hundredth?
A -;. .1. ctS /""\
lq ~ ~
o.(.;).~)
)q ;; YeL
-<2
-<j -
a. ~ 1 . 37~
@ , 3~W0
22. If a regular pentagon with 13-centimeter sides has an approximate area of
291 centimeters squared, what is the approximate length of the apothem, to the nearest
hundredth? A :: ~tLS n .;t."l I ~
'~t:j I ;;
3;.. s -3 0.. (i 3"15") '3;) S
4­
5;;, S'
tl. ~ ~.r1S
3 ~. lj v ISLI
0~q~~
23. Find the area of a regular pentagon with an apothem 5.5 meters long and a side
8 meters long.
A~ ~CLSV\
.b..";- ~ (5,S Y>'\" "(
Q ::. "()
'f')'\ '-)
«"'"y 5 J
24. Find the area of a regular heptagon with an apothem 10.4 centimeters long and a side
10 centimeters long.
A-: ;;J-<.5
Y)
';j", ::- -:z ()O,4 LV""" Ie;) Ln'\y',)
E3~~
<Yh0
25. In the figure, each circle has a radius of 7 inches. What is the area of the portion outside the
circles but inside the square? Express your answer in terms of Jr.
,A-= A-o- qAQ
A : LtD - q 1rr;J..
A";-
(4').Y4;,.) - q 'Tf(')'1-.
.A::
'/"1& 'i - 19n-)[l.Jq)
0-=: (1 /
1-£.,4- 4¥-1'1t)
;' IJ~
<E<---- 42 in . ---->~
26. In the figure, each circle has a radius of 5 inches. What is the area of the portion outside the
circles but inside the square? Express your answer in terms of Jr.
A-=An-4Ac:o
A -=-
A :.
A
<
20 in. -->~
~
(? : :
~(.} -
'-J. %-r 1­
C,.d(6)l.J.)) - Y'IT l 5)?­
'-1-00 -
eLf 60 -
(4rry'J-0
)1)0 fT
)
'il)1)
27. Find the area of a circle with radius 9 centimeters. Use Jr = 3.14. (Round to the nearest two
decimal places.) A ~.1t-'{ "2.A':.. <t I 13 . t 4.! A "0.11 ('-'1)'1II
1...
A ItJ tl6."1/ 3...,..
C/'YI
.A -;. ~ \ "Ii'
28. Find the area of a circle with radius 13 centimeters. Use Jr = 3.14. (Round to the nearest two
A~ I ~q 1.3. 14
decimal places.) ).., -rry'L
A -;. Ti ()'~)l..
A r;..., ? 30 . L:> 14 CIvI'L,
A ::. '~'1,1'i7-'
29. A circle has a circumference of 4Jrcentimeters. What is the area of the circle?
c:. -= ,;t,t r("'
Lt-1I ::: ~
~
A":.- 'it y_."l....
A
')...
~,-'1I.:;:.\~t.;):;;..
· """'-___
~1\
30. A circle has a circumference of30Jrcentimeters. What is the area of the circle?
C. -;. d 11Y
A ~ .'frJ'1. A -;. "iTLI~').. f2!0lSlI
~0
31. A circle has an area of 64Jrcentimeters squared. What is the diameter of the circle?
.A~" ' ~
l.,4 'Tt
";" 11''1-
'''1l''
1'r L 1..\ =-- .,. 1..
cl-::..02 r d .... J.W) ~
32. A circle has an area of 484Jrcentimeters squared. What is the circumference of the circle?
po... :.. ' I\Y''
2­
'!J4-1T :: 1f(
'l­
C-:-
o
~'lT L:l-?-)
4 Lf-'1 I
.:>
(ft\
33. The figure below represents the overhead view of a deck surrounding a hot tub. What is the
area of the deck? Use 7r=3.14. (Round to the nearest two decimal places.)
A-:: <1\-R 2...- 'nT' L
A c:- til (&5)7..-_ 11'(3)'2..
~~"T\
A '::
2m
- CJrt
A -: \1.0 fi'"
A~
\~
l3 , )ll)
cA ~ 50 .
.;)!.}
m~
34. The figure below represents the overhead view of a deck surrounding a hot tub. What is the
area of the deck? Use 7r = 3.14. (Round to the nearest two decimal places.)
A-- .'1\ r(}'"- 1\\1....
A
2.4 m
~ 1\
3~ ,
A ':.
.A
i ').,)2.-
~
L\q rr -
~I, ~
2.
11(3 ,3)
H),'l,'\ iT
W
A t;... :}J . i.R (3 . )4')
A
G
~
~f. , <i;;l~
-X"-t7 . 'ji.;!
0
35. Find the exact area of the shaded portion of the figure.
B
A~ A/~ -
Ao
A ~ ~bh- "t1-t~
A =- ~llq )(1 tJ1 -
16 in.
~~§§:=".c 0 Q5 ;).
A
19 in.
If (J5'i
.:l. 511
)\0
36. Find the exact area of the shaded portion of the figure.
= 3.14. (Round to the nearest two decimal places.)
tt.
1­
A
::
;;-:--lTr
•
".J llO
37. Find the area of the shaded region. Use
7r
A~ ~
1\ U;,)'L.
3~c)
A -;- ~
l ').5"Tt ")
all
A-:.
~
~ ~ £3. 14)
.A. 'X.
l.,
A ~ J3. D~ 3
~.o~'vn9
38. Find the area of the shaded region. Use
7r
= 3.14.
A -;..
(Round to the nearest two decimal places.)
P::: ",("7­
3I.Po
~;).
A ";- -3(.0 "
, .)2­
Llo
A -:. ~ l3luli) A
~
1"( -
-;(Pu­
S-
Al';:(.. ~~(3 ,'''')
S­
A t;.....
';l;;l.
lo 0<6
~.&\L"'~ 39. Find the surface area of this rectangular prism.
5A ~ !).i.vJ+ dwh -+ ;)....£h
SA ::.
SA :;
2em
10 em
(s A:C
.1 (10 )lIt))
+
abo;- '-to
~ 80
-:l( I o ) l;<} ..... :2.( 1(/)0 )
-t-
'+0
CYr1'-)
40. Find the surface area of this rectangular prism.
SA -:: (ii..L-o 4- ;J.v.:. h 4-
:l-i.h
SA ~ ...,1.(JIX,S- )-+ J(lS-:;(J,) -+
lem
;;;L(I I}(I")
SA -- 33o+- 30 r ..;22 llcm 41. Find the surface area of the right pyramid. (Round to the nearest decimal place.)
5'A ~
AD
+-
Lf.A~
SA;. fLw -+ i.f (~bh ')
9 A --
((p'U) 4-
'-I ( ~ ~ <.0Y-,)
SA -; 3<P ~ "8'4
6ft
(fA ~ \J.O [-to'-)
42. Find the surface area of the right pyramid. (Round to the nearest decimal place.)
AD
SA~
4-
LJ .AI>
SA -= .P..,w -fSA ~
(L.(t-L.O
J~
SA :
(SA'",
..,
IA
L./. C-.k)(4X(..,)
4-
~ 4
l7t bh')
$'
A0
4ft
43. Find the surface area of the cone. (Round to the nearest decimal place.)
5.A 1Iy- t. -T
-:0
'1fr ~
~ "(;Xll)+ 1\ (;,)2..
SA
S A -: l\q
(SA
iT ;-
10~1i'
:=
SA %
~q1r
cW{)
\LD~ C~ · 14 )
44. Find the surface area of the cone. (Round to the nearest decimal place.)
SA -= 1I'r..t + <"'if r
,,(~). , ••f)
SA -=
S~ A
::
~4- tT
G 'A-:
SA
(5 ~
r,:::.
I';:..-
\~
'"l..
+ 11 ( lo) "4..
-+ 3<.& IT
(y'A:J
if
1)..0 l3 ,
3--=r1,.
l~)
~
(.0
_ .- ­
......
- .,;--­
45. Solve each problem. The figures are not drawn to scale.
Area of shaded region = _
1
J
_ 1'\(10)'2­
20 em
I;
I­
.A ~ AD - Ao
A -::. ~ -If'{'z..
I dO n) ~Z-
-I
46. Area of shaded region = _ _
T
50 em
A=- Ao - Ao
A ::.
~--;nrZ
A ::::- 15 u So) -rrC:;s-)2.
~
l
r--50 em
~
47. Solve each problem. The figures are not drawn to scale.
Area of shaded region = _
..
...
1 em
A::
'TI'-- R?-- lTY''2..
A=-" (~)~
A-z..- qc,IT -
(A :
1\ 1\
IT(S,)7...
.2S-i\'"
Lrn)
48. Area of shaded region =
_
_
3cm
49. Solve each problem. The figures are not drawn to scale.
tl
Area of shaded region = _
1....J.... \
L
~ b Y)
A:
3uo 1\("
A ::
~6 If (, ') - ., ( "1 Y-, )
-
ct(}
1­
50. Area of shaded region = _ _
A -~
tl.
'2..
.3~o-n-r -
1.. \ l
;)- () h
A : . ~ TrO'5'J-- ~(It;y'/}- )
A ~ ~ (;)')5'Tr) -
¥