Quick Review

4.0 cm 2.0 cm

> We can find the perimeter of any polygon by adding the side lengths.For this pentagon:Perimeter = 4.0 + 1.5 + 2.0 + 2.5 + 2.0

= 12

The perimeter is 12 cm. ' 2.0 cm^ ^ 2.5 cm1.5 cm

> We can use a formula to find the perimeter of some polygons.Square Parallelogram Regular Hexagon

2 cm 2 cm

3 cm

P = S X 4P =2X4

= 8

P = (£ + w)X 2P = (3 + 2) X 2

= 5X2= 10

The perimeters of the polygons are 8 cm, 10 cm, and 66 mm.

T&f TIdos®

1 o Find the perimeter of each polygon.

a) b)2.5 cm

io© HS- 2oB + 3o© 4- 3o@ = 14o3 23X 3 = 73

Tlh® periimeter ns 143 cmio Th® pdromdter is 7.5 cm.

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rExploring Rectangles

25 mm

Quick Review

You can use formulas to find the perimeterand the area of this rectangle.> P = (€ + w) X 2 ¦> A = (€ x w)

= (45 + 25) X 2 = (45 X 25)= 70X2 =1125= 140

Perimeter = 140 mm Area = 1125 mm2

You can write the area in square centimetres:Use: 1 mm = 0.1 cmA= (45 = 10) X (25 = 10)

= 4.5 X 2.5

= 11.25So, 1125 mm2 and 11.25 cm2 are equal areas.

45 mm

Tir^ Tifesi

1 o Find the perimeter of each rectangle in centimetres and in millimetres.Then find each area in square centimetres and in square millimetres.

Perimeter of A: 1§o4 gm ©r mm

Area of A: 14,.# cm2 ©r moirii2

Perimeter of B: f> em m 9@ mm

Area of B: 4oi sm2 or 4S@ BTnim2

Perimeter of C: 1@.@ cm ©r 1@® mramB 30 mm C

Area of C: cm2 @r 725 Bfim22.9 cm

15 mm

A

4.2 cm

©©

Pnefi©'

1 o The perimeter of a placemat is 1489 mm. How many centimetres is that?

Miofcmi 1 com = Mif 1@ = Miof)

2. Find the perimeter and area of each rectangle.Record each measure in two different units.

si)

3.3 km 3.0 dm

2.0 km 4.1 dmSample hmwers

P = 1©oS km ®r 1© d©© m P = ICl dm ®r 142 cm

A - doi km2 m d d©© ©©© m2 A = 123 4m2 ®ir 123© em2

3o The area of a rectangular ballroom is 800 m2 and the perimeter is 120 m.What are the dimensions of the ballroom? TGne ps iruii

2© m wM<g°„ 4© x 2© — i©@g (4© + 2@) x 2 = 12©

4o The area of a rug is 8000 cm2. How many square metres is that?

©o§ wA 1 rifi)2 = H ©© cm . 'il ©© CGTTJ = 1 © ©©© ecfan2; §@©© 1 © ©©© - ©3

Stretch four ThiiScIiig

The length of a rectangle is increased by 1 unit. Its width is decreased by 1 unit.What happens to the area and the perimeter?Use an example in your explanation.

The perimeter of this r<a€tancfe h 14 €TO

and its area is 12 cm2o

(4 + 3) x 2 = 14; 4 X 3 = 12

New perimeter = 14 cm; S + 21 x 2 — 14

New mm - 1© cm2g° S x 2 - 1©

Perimeter is the same and area dtecrgases.

Sampte Answer

3 cm

4 cm

2 cm

S cm

TP

/\ . " U(§u

Quick Review

You can use a formula to find the volume of a rectangular prism.The volume is the product of the prism's length, width, and height.

Volume = Length X Width X Height

This rectangular prism is 7.0 cm long,3.5 cm wide, and 2.3 cm high.Volume = 7,0 cm X 3.5 cm X 2.3 cm 2.3 cm

= 24.5 cm2 X 2.3 cm 7.0 cm

= 56.35 cm3

The volume of the prism is 56.35 cm3.

Trv Tfcs®

3.5 cm

,7Pt

1 o Find the volume of each rectangular prism,

a)

0.5 cm3.0 cm

2.0 cm

cm3

1.2 cm4.0 cm

4 SEffi)3

«fl)

144 em3

cm1.5 cm

1.5 cm

1.5 cm

3o3T5 cm3

1.5 cm

3 cm3 1 o§ cm3

102

Praefi©'

1. Find the volume of each aquarium

a) rv=^ h)60 cm

20 cm

1.0 m

5.0 m 50 cm25 cm

40 cm©®© cm3 Dim3 31 Si® em3

2. Work with a partner.

u) Find 4 small boxes. Label the boxes A, B, C, and D.

b) Measure the dimensions of each box. Estimate, then calculate,each volume. Record your results in the table. Sample Answecrs

Box Length Width MteightEstimatedW®lume

ActualVolume

A 13,5 cm 10,5 cm <6.5 cm 75© cm3 921,4 cm3

B 9.5 cm 4.0 cm 12,5 cm 75© cm3 i3

C cm 8.0 cm 6,5 em 75© cm3 728 cm3

D 10 cm 5 cm 10 cm 500 cm3 500 cm3

3. Complete each table.

Lengtlh(cm)

Width(cm)

Height(cm)

Volume(cm3)

6 9 3 162

8 5 2 804 3 4 48

5 5 5 125

Lengtslh(cm)

Widtlhi(cm)

Height(cm)

Volume(cm3)

5.3 4.0 7.1 . J.52

6.0 3.2 5 96

10 2.0 1.1 22

12.0 2.5 4.0 120

Streteii T®ir Tiiiilciei|

Jocelyn built a rectangular prism with 36 centimetre cubes.What might be the dimensions of the prism? Give as many answers as you can.

1 x 1 x P x 2 x li° n x 3 x 12g 1 x 4 x f)B°

1 x § X (§; 2X2X9; 1 X 3 X 3X3X4

coro

/ The Cubic MetreW

Quick Review

A line segment has only one dimension.It is measured using linear units such as centimetres and metres.

A flat surface has two dimensions.The area it covers is measured using square units such as squarecentimetres or square metres.

An object has three dimensions.The space it occupies is measured using cubic units suchas cubic centimetres or cubic metres.

.OAs %fe"

A cube with edge length 1 m has volumeone cubic metre, or 1 m3.1 m3 = 100 cm X 100 cm X 100 cm

= 1 000 000 cm3

1 m

1 m1 m

To find the volume of a rectangular prism in cubic metres, we findthe product of the length, width, and height in metres.Volume = 3.0 m x 2.0 m X 2.5 m

= 6.0 m2 X 2 5 m= 15.0 m3

The volume of this prism is 15 m3. 3 g m2.0 m

2.5 m

Tcf ¥Gi@$(s

1 c Would you use a linear, square, or cubic unit to measure?

u) area of a desk pad square yroit b) space in an elevator cubic unit

c) length of a pen iliBiear unit d) perimeter of a dog run linear unit

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