Module 4 answer key for homework

1. Module 4
Answer rey

2. a a ES
3 ©

Name Date,
1. Magnus covers the same shape with angles, rhambuses, and trapenids

a. How many tranges wilt take to cover the shape?

LA tages

ba. How many hombuses wilt take to cove the shape?

€. Magnus notices that tiangls from Par) cover 1 trapezid. How many trapezoid wil take to
‘cover the shape below? Explain your answer.

Fons

I BEN mente engage" uO

CS AAN

3. E)

2. Angela uses square to find the rea o rectangle. Her works shown below.
3. How many squares ld she use to cover the rectangle?

AZ. sas

a. Wiatis the area ofthe rectangle in square units? Explain how you fund your answer.

The area oF the rectangle ie 12 equare unde,

4 does Ae quero do cover Me
> a

N free rte

oe _
1 x16=10
cames
mes

ko: 18
BB

echange À has the largest area at 18 quae units,
18 is larger than 8 or 10 +

‘aa en

engage"

Wann unse CE ct

4. >

Name Date,

Sl re
ne = ;

5. TIEREN
©

2. Col uses square inch plces to create these rectangles, Do they have the same area? Ela.

eee 4,

min.
No, the rat je has an area E Som
hosecond vechame has an area & Gg

sl rer
ee

|

Le ay units

©

EQMMON | wens rn cnn ex ny \

6. Name Dat,

1. Each [_]11 square unt, Wnatis the area of each ofthe flowing rectangles?

1

DRE Ho een es

> Rens

ques units

eS AA =

prey

7. à nef Jenn woman tne nisin

©
an (ant ee oe
Bee Se engage” u

8. Name Date

1. Ella placed square-cntimeter tes on the rectangle below, and then labeled the ide lengths. What the
area of hor rectangle?

Total ares A ges m

2. Kyle ses square-centmeter testo find the side lengths ofthe rectangle below. Label each side length.
‘Then count th tes to find the total area.

dag em.

“otal ares

3. Maura uses squareinch les to find the sido lengths ofthe rectangle below. Label each side length. Then
find tho total area. E

230.

terme 11 guarani -

COMMON | umune neutro rotar ls ono
CORE

= engage" re)

9. 4. Each square unt below 1 square inch, Claire says thatthe side length ofthe rectangle below 3
Inches. Tyler says the cido length is Sinches. os correct? Explain how you know.

- Gath are correct. There ore 5 in. alang the top,
? Gd 3 4-0: 2) dow he sida,

5. Label the unknown side lengths forthe rectangle below, then nde ren. Explain how you used the
lengths provided to find the unknown lengths and ares,

Ainches sp ‚ne siden d 0
tehooge os equal M
leven.
tee re

— Hinds

> TOR en CA
mens mn,

10. 1. Usethecentimetr side of a ruler to draw athe tes, then tip-counttofnd the unknown side length or

area, Write amulipcation sentence fr each ted rectangle.

«ssn gn 8A rame
sem E
HHH =

sx 6. n

5) © Ares: 28 square centimeter ext. dt

+
i

engage" «x

11. ©

2. Ali makes a rectangle wth 45 square-nc ls. She oranges the ls n equal rows. How many
squareinch tes are In ach row? Use words, cur, and numbers to support your answer.

483624
here ose A Riles in each wads

La
em

3. Leonmatas recae WS square timer es, There reno ots.
How mn ar exchrov? ‘Use word pci ed number spor or ne

| E Pee
Hagen There ace 4 eo in each vas
©
Inge
8. Con range el agua animal equa ows Ure wor, pures, and
Si - 367626
Leon con arrange all 2 %.0m,
Sew Ales mo 6 epa mos E Óhtes
in cod ya.
© Dove nf) and () have the same total area? Expatn how you know.

Yes, both reckanles in a. and lo, haye the same total
area. 9x4= Bo and CXG= 3b. 4-2

aS AA

engage” lO
eee ER a as

12. Name Date,

1. Each CJ represents a 1-cm square, Draw to find the number of rows and columns In each array. Match it
o Rs completed array. Then fin the blanks to make true equation to find each array area.

og Dye by [En œ

gen E y 55 Sam

AB lb am

a DL Zum

loro Ham

2.8 ¿Lam

engage" «2

13. 2. Minh skp counts by shes to find the total square uns in the rectangle below. She says there are 36

square un. she core? Bi ou answer nes
6x6= 36

Mon o correr, There are Bb ej.uniba
€ I in rs rectangle.

“The tub in Paige's bathroom covers th tle floor as shown below. How many square tes ae onthe
oor, ncuding te tes under the tub?

22 Qx10= 90
There are 90 spe Kles on the
Asor in ah.

»

O

4 Frankseesa book on top of his chesshoard, How many squares ar covered by the book? Explan your
answer, 6x6: 3b

here are 36 equares corad by de

14. Nome Date

1. Find the area of ach rectangular array. Label the side lengths ofthe matching area model and we a
‘multiptetion equation foreach area mode.

ÉTEINT ES ‘rea Model

Dorn NEED)
(@)
se j Fe :
Be

= me

TI SQMMON | sun sam tence

engage” O

es en nent CE cenit

15. À

3. lan arrange square pattern blocks nto 7 by 4 array. Draw las array onthe the grid below. How
‘many square units are In tans rectangular array?

4x7: 28

El

There are 28 square
la aiiarts ee

any.

abel he side lengths of ans aray fom Part a) on the rectangle below. Then wre 2
mutation sentence to represent the area ofthe rectangle.
Y

Yx7=28

4. ona raw 926

tr rectangle. Gregory draws 226 square inch rectangle. Whose

‘rectangle larger in area? How do you know?

Gregory'®

rechange o layger because inches axe

larger nan centimeters .

Y En

ne on engage"
an,

16. 2. Write a muktplcation sentence to find the ares ofeach rectangle.

ft sch

HT eis fat

2. Wette a muttipetion sentence and a dlvson sentence to find the unknäum side length for each
rectangle,

17. 2. Onthe grid below draw a rectangle that has an area of 32 square centimeters. Label the side lengths.

LBS] 4x82 32 5.0m.
3

O

3.. Patricia draws a rectangle that has id length o 4 centimeters and 9 centimeters. Whats the area of
‘the rectangle? Explain how ou found your a

es
1x4= 36

as The area of the rectangle is (O
36 mem. L ae he length

oF the Sides do ger the area,

4. Charles craw a rectangle with aside length of inches and an are of 27 square inches. Whats the
‘other side length? How do you know?

Lind a1: 923
ee] Laure
3x4= 27.
en O)

18. Name Date

1. Use he gid to answer the questions below.

a. Drewa Ineto show how to vide the grid nto 2 equal rectangles. Shade Ino the rectangles.

Label the side lengths of each rectangle,

Wlan juan show te total arn of the 2 tangles ö
4x8: 32 SR+Se= Gt or Bx B= ot
4x8 = 32. The Hal area of the 2 redamgle

vie CA sy onto,

COMMON | aces se tren mens 0 sad es
CORE me ss

engage” «LO

19. 2. Alexa cuts out the 2 equal rectangles from Problem (a) and pat the two shorter sides together,
8. Draw Ales new rectangle and label the ido lengths below.

¡|

b. Find the total area of the new, longer rectangle. he on Bay
E 5 e \ area nao
de xt = (020) x) reckange 13 EJ og unta,
co + 2%
8

"

©
"

c._Isthe area of the new, longer rectangle equal to the total area In Problem 1(c)? Explain why or why
E
Yes, both vectanges have the same ara because

Me pieces were We same, ur pa haser
different ,

Dre

engage" sem

mm AN

20. Name Date

1. Label the ide lngihs of the shaded and unshaded rectangles. Then find the total are of the large
rectangle by adding the areas ofthe 2 smaller rectangles.

a ls 4
s
unst_JD sas
4 10 LD 25)
«50 10
= GO sureunts
Sram
=(5x8)+(4x8)
= "40.32 2
) = 12 sree
e a 3 a 10 2
EH
7
q
Teer ID 29
0 /0)+0%3) ENTER)
+710. al : +910 +6» 2.)
«U squereunts +10 +18
= 108 square units

Popo ara ony e ro

ns: engage” “ez
A

21. 2. Fimimagins 1 more row of ine to find the total area of «9 rectangle. Explain how this could hep him
sobe929,

q

Finn can now save Ax 10 = {D

mins 1x4 which = 81 er une

a See eg rae à make rere om Pad m ofa mo ot ez O
Yxle> +xC046)
(tx 10) + exe)

HO +:
= GH une.

= droided Me larger rectangle He soto
4X1 and Mn eee Whe areas
of he OO gmaler rec:

© Jaded nom Sogether do gor
Abe larger recrana\e.

u

v

les and
area À

COMMON

tent: spb art ropa nr Rd ect
CORE ieee bree ct
ps

engage” ssi?

sc
ms:

22. Name Date,

1. The rectangles below havethe same area. Move the }tofind the missing ide length Then solve.

Jem EAN LR RE
bares: 1436" 36 sqem

Ba
Be 2 ETRE

aan ban 9 (2x2
nas)
a an 4x In 36 cn RE

Bo

em
AZ

à nee sade (6n2)x3

© Area: 4x9=4x (3x3) ax)
dida GA
"12:32 = 36 um
- 26 um

2. Does Problem 1 show sl he possible whole number sde length fora rectangle with an area of 36
square centimeters? How do you know?

Yes, there are no other Waste numbers that you can
mati do aqu 26,

MB Ea engage" dl)
a

23. a. Find the area of the rectangle below.

na 8x0: 48 g.em.

Bb. Hide says a4 em by 12 en rectangle has the:
‘equation to ind the related fact and solve. I

es asthe rectangle In Par (a. Place {Jin the
facorrect? Why or why not?

Anizuan2us pida io correct. 1x2 98
hades er AD jut as BXC: A8,
Eb = 4x2
um Es

I. iento ng range at une run
‘rectangle In Part (a). Show your equations using (). Then estimate to draw the rectangle and label

Lori
8x6= BXAXD 8X 6= (UxDxb
= (8x2 x3 = 4X2xe) ts
= Iex3 ptm le
e = 48 is

2 Mo: 8x6= (axe
= axl4x

Lu sexed

= 48

> Tw’ [eee Seen engage" seu

24. ate
1. A squarecalendarhassidesthatare inches long, Whatlsthe calendar ares?

Qu | axa 8l The calendars area io

a sy Inchon +

2. Each gts 3 square uni sienna uses the same square unis to draw a 6 x 2 rectange and says that

I has ho same ara a the rectangle below. I she correct? plain why or why not.

Yes. HxB212 punis:

Gx2= 12 GE Ben nr
an area & EB une,
ne unite amis
arrangeh at

3. Thesurface ofan office des has an area of 15 square feet is legis 5 feet, How wide ls th office
ek? E

She 16:53

Em) Rome.

Sr

engage" 402

25. 4, Arectongulor garden has a total area of 48 square yards. Draw and label two possible rectangular
Gardens with diferent sda lengths having the same area.

\2

or 12x4= 48
4
2° 2x24: 48
à FT mr
na

$. arith pet e, Pd pn ar aan, Ten eth er pr

ae
À
= E

Ivzsz zur KEG es BG yes 10

Éadn Hime Ula adde anser tao of 2. The area
F the Figures goes up oy 2 aa doma

COMMON | ese carne on ny

©

Poe)

26. ©

A LE + 7» 24 sou
Figure: Areactcsaresoto: PH RO Y guns
Feos: aractevarnctt: 2. BZ. 44 ui

Figure: AraotGraresott: 1D + RD 2 HO saunts

COMMON | soni pda amp ii career cop compo
CORE

RES engage” i

mes CE mamans

27. 2. Thefigre shows a small rectangle cut outofabigrectangle. Find the aren ofthe shaded region.
Tem

vcectvestadsreon: SO 9. AT cn

3. The figure shows a small rectangle cut out of abigrectangle.

tbe he mig mestremente
h Aenotthesigrecunge: | 8 72 soon

«.Areofthesmatrecange: 3 4 + [2_saen

à Find the area ofthe shaded region.

7a
712

co yen

e cr e mp po

mM
nen engage”Y «ou

© TBR SQMMON |

28. 1. Find the area of ech of the following gues. Al figures are made up of rectangles.

6x8= 48 2 Pet
ara a7 m hal
UB + 27= 75 aya.

sea The area & the figure
a 15 q há.

3x8= 64 ay in.

zxe= ban

64-6= 58 aun.
The area eE ie Faure
is Bam.

ON na
N [mee penedes
O | et engage” sos

29. 2. Thefigur below shows a small rectangle cut out ofa big rectangle,

a. Labelthe side lengths ofthe unshaded region.

ba. Findth are of the shaded region,

©

ID x= TO oy feet Hr ho ane)
ars x = region 19 88 sy fest,

Sip
aioe
55 a
IR SON | = Fe ny

Fe)

30. Name Date

Jeremy plans and designs is un dream playground on grid paper. Hi new playground wil cover a total
area of 72 square uns, The chart shows how much space he gives foreach plece of equipment, or rez. Use
‘the information in the chat to draw and label a posible way Jeremy ca pan his playground.

©