W2 - Lesson 3: Perimeter and Area · Area Area is the amount of surface a figure covers. Square...

Mathematics Grade 6 TEACHER KEY

W2 - Lesson 3: Perimeter and AreaV5-07

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Mathematics Grade 6Version 5Preview/Review W2 - Lesson 3 TEACHER KEY

Publisher: Alberta Distance Learning CentreAuthor: Elgin PawlakIn-House Teacher: Sue Rees

Project Coordinator: Dennis McCarthyPreview/Review Publishing Coordinating Team: Nina Johnson, Laura Renkema, and Donna Silgard

W1 - Lesson 1 ............................................................. Basic Facts, Basic Operations, and IntegersW1 - Lesson 2 ............................Place Value, Whole Numbers, Decimals, and Common FractionsW1 - Lesson 3 ..................................................................Improper Fractions and Mixed NumbersW1 - Lesson 4 ....................................................................................................Ratios and PercentsW1 - Lesson 5 ...........................................................................Number Operations with DecimalsW1 - QuizW2 - Lesson 1 ........................................................... Factors, Multiples, and Prime FactorizationsW2 - Lesson 2 ................................................................................................. Metric MeasurementW2 - Lesson 3 .................................................................................................... Perimeter and Area W2 - Lesson 4 ...........................................................................................Surface Area and VolumeW2 - Lesson 5 ..........................................Working with Angles and Drawing Objects and ShapesW2 - QuizW3 - Lesson 1 ......................................................................................................... TransformationsW3 - Lesson 2 ...........................................................Bar Graphs, Line Graphs, and Circle GraphsW3 - Lesson 3 .................................................................................. Collecting and Analyzing DataW3 - Lesson 4 ......................................... Number Patterns, Magic Squares, and Problem Solving W3 - Lesson 5 ..........................................................................................Probability and OutcomesW3 - Quiz

Materials Required: A textbook is not needed. This is a stand-alone course.

Important Concepts of Grade 6 Mathematics

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Preview/Review Conceptsfor

Grade Six Mathematics

TEACHER KEY

W2 - Lesson 3:Perimeter and Area

OBJECTIVES

By the end of this lesson, you should

• understand the perimeter as the distance around a figure

• understand area as the size of a surface

• use metric units of measure to determine perimeter and area

GLOSSARY

area - the amount of surface afigure covers

parallelogram - a variation of arectangle, but opposite anglesare equal

perimeter - distance around anyshape

polygon - a straight-sided figurewith three or more sides

quadrilateral - a straight-sidedfigure with four sides

rectangle - a variation of asquare, but opposite sides areequal

square - a figure with four equalsides and angles

Developed by Alberta Distance Learning Centre .............................................................................................................. 1

Preview/Review Concepts W2 - Lesson 3 Mathematics Grade 6 - TEACHER KEY

W2 - Lesson 3: Perimeter and Area

Welcome to W2 - Lesson 3! This lesson is about perimeter and area. Youwill use your skills in metric measurement to find lengths and areas. Thelesson has three topics:

• Perimeter• Area• Areas of Irregular Shapes

Have fun with shapes and sizes!

Perimeter

The distance around any shape is its perimeter. Perimeter is found byadding the lengths of all sides of the figure. Perimeter is usually measuredin kilometres, metres, centimetres, or millimetres.

All straight-sided figures with three or more sides are called polygons. Thenames of some common polygons are given in this chart.

Special quadrilaterals that you can see frequently include the following:

Square - All four sides and angles (corners) are equal.

Rectangle - Opposite sides are equal, and all angles are equal.

Parallelogram - Opposite sides are parallel and equal, but pairs ofopposite angles are equal.

sediSforebmuN nogyloPfoemaN

erugifdedis-3 elgnairt

erugifdedis-4 laretalirdauq

erugifdedis-5 nogatnep

erugifdedis-6 nogaxeh

erugifdedis-7 nogatpeh

erugifdedis-8 nogatco

Preview/Review Concepts W2 - Lesson 3Mathematics Grade 6 - TEACHER KEY

............................................................................................................. Developed by Alberta Distance Learning Centre2

Questions

1. Find the perimeter of the following polygons. Write the formula (suchas 8 + 4 + 4 = 16) each time and always write the units of measurementin your answer. (km, m, cm, or mm)

a.

b.

c.

d.

4 cm

6 cm6 cm

12 mm

10 km

14 km

40 mm

55 mm

6 + 6 + 4 = 16 cm

12 + 12 + 12 + 12 = 48 mm

10 + 10 + 14 + 14 = 48 km

40 + 40 + 55 + 55 = 190 mm



e.

f.

g.

h.

85 mm50 mm

70 mm

6 m

24 m

6 mm

4 mm

8 mm

6 mm

6 + 8 + 6 + 4 = 24 mm

11 + 22 + 22 + 11 + 22 + 22 + = 110 cm

6 + 24 + 6 + 24 = 60 m

50 + 85 + 70 = 205 mm

22 cm

22 cm

11 cm

11 cm

22 cm

22 cm



2. Use a ruler to measure the sides of the following polygons, and writethe lengths on the figure. Then, find the perimeter of each. Write youranswers in centimetres.

a. b.

c. d.

e. f.

4 cm

2 cm

P = 12 cm

P = 13 cm

P = 20.4 cm

P = 12 cm

P = 11.2 cm

P = 19.4 cm

6.7 cm 6.7 cm

6 cm

2.8 cm

2 cm

2 cm

2 cm

2.5 cm

3.7 cm1 cm

4 cm

2.5 cm



3. Calculte the perimeter for each polygon. Use the space below to doyour calculations.

erugiF foepyTnogyloP sediSfohtgneL retemireP

A elgnairt,m8.71,m1.31

m4.41 m3.54

B erauqs mm55 mm022

C elgnatcer mc6.7,mc7.4 mc6.42

D margolellarap mc42,mc36 mc471

Eraluger*nogatco

m61 m821

F nogaxeh6.3,m0.4,m5.1,m8.5,m2.5,m

m8.2m9.22

.sedislauqethgiesahnogatcoralugerA*



4. Calculate the perimeter for each polygon. Note carefully the units ofmeasurement. Write all the answers in centimetres. Use the spacebelow to do your calculations.

erugiF foepyTnogyloP sediSfohtgneL )mc(retemireP

A elgnairt,mc871,m1.3

mc441+mc871+mc013

mc236=mc441

B laretalirdauqmm321,mm56mc5.81,mc51

+mc3.21+mc5.6mc5.81+mc51

mc3.25=

C nogatnep,mc6.7,mc76

mc76mc45,mc45

mc76+mc6.7+mc76mc45+mc45+

mc6.942=

D nogaxeh

221,mc42,mc36,mm

33,mc15,mm431mc

2.21+mc42+mc36+mc15+mc4.31+mc

mc6.691=mc33

E nogatco

7,m81,m9,m61,m

,mc345,mc432mc247,mc034

+mc009+mc0061+mc007+mc0081

+mc345+mc432+mc345+mc034

mc247+mc034mc9496=

430 cm + 742 cm= 6949 cm



Area

Area is the amount of surface a figure covers. Square units are used tomeasure area.

mm² = square millimetrescm² = square centimetresm² = square metreskm² = square kilometres

Formula for Area of Quadrilaterals

Because quadrilaterals are regular figures, formulas are useful to calculatearea.

Rectangle:Area = base × heightA = b × h (abbreviated form)A = 5 × 3 = 15 cm²(Count the squares.)

Parallelogram:Remember: Height means thevertical height - the distance upand down.

A = b × hA = 5 × 2 = 10 km²

Triangle:A triangle is one half a rectangle.

Area = 12

base × height

A = 12

b × h

A = 12

(2.5 × 4) = 12

(10) = 5 cm²

base 5 cm

height3 cm

height2 km

base 5 km

height4 cm

base 2.5 cm



A = 12

b × h

A = 12

(5 × 6) = 12

(30) = 15 km2

Note: The height is the vertical height.

A =12

b × h

A = 12

(25 × 40)

A = 12

(1 000)

A = 500 mm²

Remember: The height is the vertical height.

height6 km

base 5 km

height25 mm

base 40 mm



6 km

8 km

30 mm

18 mm

Questions

1. Use the correct formula to calculate the area of each of the followingpolygons. Write your answer in square units (mm², cm², m², or km²).

a. b.

c. d.

4 cm

5 km

12 km

2

A = b × h= 8 km × 6 km= 48 km 2

A = b × h= 18 mm × 30 mm= 540 mm

2

A = b × h= 4 cm × 4 cm= 16 cm

2

A = b × h= 12 km × 5 km= 60 km



e. f.

g. h.

42 mm

61 mm 18 km

10 km

36 mm

47 mm

3.5 km

5 km

2

2

1A (b h)

21

A (36 mm 47 mm)21

A (1692 mm )2

A 846mm

= ×

= ×

=

=

2

2

1A (b h)

21

A (5 km 3.5 km)21

A (17.5 km )2

A 8.75 km

= ¥

= ¥

=

=

2

2

1A (b h)

21

A (10 km 18 km)21

A (180 km )2

A 90 km

= ¥

= ¥

=

=

2

A = b × h= 61 mm × 42 mm

= 2 562 mm



2. Calculate the area of each polygon. Write your answer in square units(mm², cm², m², or km²). Use the space below to do your calculations.

Figure Type of Polygon Base Height Area A Triangle 22 mm 12 mm B Square 17 cm C Rectangle 23 m 11 m D Parallelogram 18 km 25 km E Triangle 30 m 22 m F Rectangle 112 mm 200 mm G Parallelogram 33 cm 44 cm

erugiF foepyTnogyloP esaB thgieH aerA

A elgnairt mm22 mm21 mm231 2

B erauqs mc71 mc982 2

C elgnatcer m32 m11 m352 2

D margolellarap mk81 mk52 mk054 2

E elgnairt m03 m22 m033 2

F elgnatcer mm211 mm002 mm00422 2

G margolellarap mc33 mc44 mc2541 2



3. Determine the area of each polygon. Note carefully the units ofmeasurement. Write your answer in square centimetres (cm²).Hint: You should convert all mesurements to cm before completing thecalculations.

erugiF foepyTnogyloP esaB thgieH mc(aerA 2)

A elgnairt mm08 mc21 mc84 2

B erauqs m4.0 m4.0 mc0061 2

C elgnatcer m53.0 m55 mc5.291 2

D margolellarap mm42 md4 mc69 2

E elgnairt m0.1 mc2.2 mc011 2

F elgnatcer mm29 mc23 mc4.492 2

G margolellarap mc34 mc41 mc206 2

2m



4. Use a ruler to measure the base and height of each of the followingpolygons and then calculate the area. Your measurements should bewithin 2 mm of the correct answer. Measure carefully!

a. PERIMETER AREA

12. 5 cm (approx)

b.

20 cm

c.

d.

4 cm

5 cm

3.5 cm

5 cm

5 cm

5 cm

5 cm

4 cm

2.5

h 18 cm

9 cm

3 cm

24 cm

4 cm

25 5 25 cm¥ =

× = 22.5 5 12.5 cm

23 9 27 cm¥ =

= × ×

= 2

13.5 4

2

7 cm



Areas of Irregular Shapes

Finding the areas of figures that are not triangles, rectangles, orparallelograms is a challenge for you. You likely see that this figure belowis actually two rectangles–one larger than the other.

Figure ABCDEFG is not a regular polygon but it can be viewed as tworectangles. Then, the areas can be added to find the total.

Area of rectangle ABFG = b × h = 4 × 3 = 12 cm²Area of rectangle CDEF = b × h = 3 × 2 = 6 cm²Total area = 18 cm²

A

G F

B

C D

E

4 cm

3 cm

2 cm

3 cm



Questions

1. Find the perimeter and area of each of the figures below.

a.

b.

c.

G

M

H

K

L

12 cm

19 cm

7 cm

3 cm

7 cm

A

E

B

E

D

2.5 cm

3 cm

4.5 cm

2 cm

6 cm

4 cm

3.2 cm1.3 cm

1.5 cm

1 cm2.8 cmF

GH

J

C D

1.5 cm

( ) ( )( ) ( )

= × + ×= × + ×= +

=

=

2

A b h b hA 12 7 7 3

A 84 21

A 105 cm

Perimeter 52 cm

( ) ( )

( ) ( )

= × + ×

= × + ×

= +

=

=

2 2

2

1A b h b h

21

A 4.5 cm 3 cm 3 cm 2 cm2

A 13.5 cm 3 cm

A 16.5 cm

Perimeter 17 cm

( ) ( )( ) ( )

= × + ×

= × + ×

= +

=

=

2 2

2

A b h b h

A 6 cm 1 cm 4 cm 1.5 cm

A 6 cm 6 cm

A 12 cm

Perimeter 19.5 cm



2. Draw a polygon with the following characteristics.

a. rectangle with a perimeter of 12 cm and an area of 8 cm²

Exact measurement of 2 cm by 4 cm rectangle.

P = 4 cm + 4 cm + 2 cm + 2 cm = 12 cm.

2

A = b × h= 4 cm × 2 cm= 8 cm

b. square with a perimeter of 24 cm and an area of 36 cm²

Exact measurement of 6 cm on each side.

P = 6 + 6 + 6 + 6

P = 24 cm

6 cm

6 cm

2 cm

4 cm



Homework Assignment

1. Find the perimeter and area of the following figures.

a.

b.

10 mm

10 mm

20 mm

40 mm

7 km

16 km4 km

2 km6 km

9.5 km

2

2

2

2

P 200 mmA 40 mm 40 mm 1600 mm 20 mm 10 mm 200 mm 20 mm 10 mm 200 mm

A 2000 mm

=

= × =

= × =

= × =

=

2000 mm2

( ) ( )= × + ×

= +

=

=

2 2

2

1A 7 km 9.5 km 4 km 15 km

2A 66.5 km 30 cm

A 96.5 km

Perimeter 54 km



55 cm

55 cm

15 cm28 cm

20 cm 13 cm

22 cm

c.

d.

46 mm

52 mm

90 mm

45 mm

25 mm

25 m

m( ) ( )

( ) ( )

= × + ×

= × + ×

= +

=

=

2 2

2

1A b h b h

21

A 25 mm 46 mm 90 mm 45 mm2

A 1150 mm 2025 mm

A 3175 mm

Perimeter 283 mm

( ) ( ) ( )( ) ( ) ( )

= × + × + ×

= × + × + ×

= + +

=

=

2 2 2

2

A b h b h b h

A 55 cm 13 cm 55 cm 22 cm 55 cm 15 cm

A 715 cm 1210 cm 825 cm

A 2750 cm

Perimeter 250 cm



Self-Evaluation

Ask yourself some important questions. Write your answers insentences for your teacher.

1. In this lesson, what part of your work was excellent?

2. In this lesson, what part of your work needs improvement?

3. If you want help for some of the work in this lesson, ask your teacherin this space.

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W2 - Lesson 3: Perimeter and Area · Area Area is the amount of surface a figure covers. Square...

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