Hinterland Area/ perimeter

Problem-SolvingProblem-Solving

R U P C ?Read it! … what’s it about?

Underline it! … find the clues

Picture it! … add? subtract? multiply? divide?

… use a number line to help

Calculate it! … work it out !

How to become How to become aa PROBLEM-CRACKERPROBLEM-CRACKER

inin 4 Easy Steps! 4 Easy Steps!

The Area of a Rectangle …The Area of a Rectangle … means … the amount of surface inside and measured by … the number of squares inside (eg: square centimetres, square metres, square feet, square yards)

- Or LENGTH X WIDTH- Or LENGTH X WIDTH

= 10 X 6 = 60

The area is 60 square The area is 60 square metresmetres

- Or ROWS X COLUMNS- Or ROWS X COLUMNS

6 rows of 10 squares = 60

The area is 60 square The area is 60 square metresmetres

COUNT THE SQUARESCOUNT THE SQUARES

1, 2, 3, … 59, 601, 2, 3, … 59, 60

The area is 60 square The area is 60 square metresmetres

10 m

6 m

Area Example 1 Area Example 1

Easy! Just count the 12 squaresEasy! Just count the 12 squares

Area = 12 squares centimetresArea = 12 squares centimetres

METHOD 1: COUNT THE SQUARESMETHOD 1: COUNT THE SQUARES

USEFUL METHOD WHEN …USEFUL METHOD WHEN …

- You can see the squares - You can see the squares

ANDAND

-therethere’’s not too many to count!s not too many to count!

What is the area of this rectangle? …

HOW MANY SQUARES?

What is the area of this rectangle? …

HOW MANY SQUARES?

Too many squares to count!Too many squares to count!Is there an easier way?Is there an easier way?

You can see there are 6 rows with You can see there are 6 rows with 10 in each row 10 in each row = 60 squares= 60 squares

METHOD 2: AREA = ROWS X METHOD 2: AREA = ROWS X COLUMNSCOLUMNS

USEFUL METHOD WHEN …USEFUL METHOD WHEN …

- You can see the squares - You can see the squares

BUT BUT

-therethere’’s too many to count!s too many to count!

Area Example 2Area Example 2

Area Example 3 Area Example 3

What is the area of this rectangle? …

HOW MANY SQUARES?

What is the area of this rectangle? …

HOW MANY SQUARES?

No squares to countNo squares to count

BUTBUT

7cm means 7 squares fit in each row7cm means 7 squares fit in each row

5 cm means 5 squares fit in each column 5 cm means 5 squares fit in each column 22

Number of squares = length x widthNumber of squares = length x width = 7 x 5 = 35 square centimetres= 7 x 5 = 35 square centimetres

METHOD 3: AREA = LENGTH X WIDTHMETHOD 3: AREA = LENGTH X WIDTH

USEFUL METHOD WHEN …USEFUL METHOD WHEN …

- You can- You can’’t see the squares t see the squares

ANDAND

ItIt’’s very fasts very fast

7 cm

5 cm

9 cm

3 cm

AREA = AREA =

LENGTH X WIDTHLENGTH X WIDTH

AREA = COUNT AREA = COUNT THE SQUARES THE SQUARES

AREA = AREA =

ROWS X COLUMNSROWS X COLUMNS

Area: Test Yourself 1Area: Test Yourself 1

Which method

best suits each

problem?

Which method

best suits each

problem?

AREA = AREA =

LENGTH X WIDTHLENGTH X WIDTH

Area: Test Yourself 1Area: Test Yourself 19 cm

3 cm

= 9 x 3 = 9 x 3

= 27 cm= 27 cm²²

= 4 x 2 = 4 x 2

= 8 cm= 8 cm²²

= 11 x 5 = 11 x 5

= 55 cm= 55 cm²²

AREA = AREA =

LENGTH X WIDTHLENGTH X WIDTH

Area Test Yourself 2Area Test Yourself 2

ANDwhich way works for

ALL 3?

ANDwhich way works for

ALL 3?

8 cm

5 cm

= 7 x 5 = 7 x 5

= 35 cm= 35 cm²²

= 8 x 5 = 8 x 5

= 40 cm= 40 cm²²

= 3 x 4 = 3 x 4

= 12 cm= 12 cm²²

Area– General Rule for all Area– General Rule for all RectanglesRectangles

General Rule:General Rule:

The area of a rectangle = Length x The area of a rectangle = Length x WidthWidth

Or if you like shorthand …Or if you like shorthand …

A = L x WA = L x W

The Perimeter of a Rectangle …The Perimeter of a Rectangle … means - the distance around the outside and is measured by - the sum of the lengths of the 4 sides (eg: millimetres, centimetres, metres, kilometres, feet, yards)

2 LENGTHS + 2 WIDTHS 2 LENGTHS + 2 WIDTHS

= 2 X 10 + 2 X 6= 2 X 10 + 2 X 6

= 20 + 12 = 32m

ADD 1 LENGTH + 1 ADD 1 LENGTH + 1 WIDTH THEN DOUBLE ITWIDTH THEN DOUBLE IT

10 + 6 = 16m10 + 6 = 16m

2 X 16 = 32m2 X 16 = 32m

ADD 4 LENGTHS IN ADD 4 LENGTHS IN ORDERORDER

10 + 6 + 10 + 6 = 32 m10 + 6 + 10 + 6 = 32 m10m

6m

10m

6m

PerimeterPerimeterUnits of perimeter: Units of perimeter:

Any units of lengthAny units of length

METRIC UNITSMETRIC UNITS

Millimetres mmMillimetres mm

Centimetres cmCentimetres cm

Kilometres kmKilometres km

IMPERIAL UNITSIMPERIAL UNITS

Miles Miles

YardsYards

FeetFeet

InchesInches

STEP 1

Read it !

STEP 2 Underline

it !

… and …LOOK FOR

KEY NUMBERS

!

The history

classroom is 10m

long and 4m wide.

How much carpet

is needed for the

floor?

WORD CLUE! area

KEY NUMBER!

KEY NUMBER!

… and WORD CLUES – area or

perimeter?

AREA CLUES

surface

cover

coverage

amount of carpet

how much carpet

Some word clues to watch out

for…

PERIMETER CLUES

edge

edging

outside distance

outside length

perimeter fencing

total outside length

external length

STEP 1 Read it !

STEP 2 Underline It !

STEP 3 Picture It! !

The history

classroom is 10m

long and 4m wide.

How much carpet

is needed for the

floor?

WORD CLUE! area

KEY NUMBER!

KEY NUMBER!

10m

4m

This means AREA

Example 1STEP 1 Read

it !

STEP 2 Underline It !

STEP 3 Picture It! !

STEP 4 Calculate It !

Area of a rectangle = length x width

= 10 x 40

= 40

An area of 40m ²² carpet is needed.

10m

4mThe history

classroom is 10m

long and 4m wide.

How much carpet

is needed for the

floor?

STEP 1

Read it !

STEP 2 Underline

it !

… and …LOOK FOR

KEY NUMBERS

!

The history

classroom is 10m

long and 4m wide.

How much edging strip is

needed for the

classroom floor?

WORD CLUE! perimeter

KEY NUMBER!

KEY NUMBER!

AREA CLUES

surface

cover

coverage

amount of carpet

how much carpet

PERIMETER CLUES

edge

edging

outside distance

outside length

perimeter fencing

total outside length

external length

… and WORD

CLUES – area or

perimeter?

STEP 1 Read it !

STEP 2 Underline It !

STEP 3 Picture It! !

Example 2Example 2

10m

4m

10m

4mThe history

classroom is 10m

long and 4m wide.

How much edging strip is

needed to go around the classroom floor?

This means PERIMETER

10m

4m

10m

4m

Remember – there’s lots of ways to do this!

For example: 10 + 4 + 10 + 4 = 28

OR 10 + 4 = 14 2 X 14 = 28

OR 10 X 2 = 20 and 4 X 2 = 8 20 + 8 = 28

Remember – there’s lots of ways to do this!

For example: 10 + 4 + 10 + 4 = 28

OR 10 + 4 = 14 2 X 14 = 28

OR 10 X 2 = 20 and 4 X 2 = 8 20 + 8 = 28

The history room floor

is 12m by 6m.

The project corner is a

1m by 3m rectangle.

The rest is tiled.

How much of thefloor surface is

tiled?

WORD CLUE! area

KEY NUMBER!

KEY NUMBERS!

Total Area = 6 + 9 = 15m²

The tiled area is 15m ²

1m

6m

3m

3m

Example 4STEP 1 Read

it !

STEP 2 Underline It !

STEP 3 Picture It! !

2 Steps so far …

CLICK for Step 3!

EDGING MEANS PERIMETERBut the shape you’re interested in is not a rectangle!

One way is to start at the top left-hand corner and write down each length around the perimeter.

Then ADD.

The history room floor

is 12m by 6m.

The carpeted area in the corner is a

1m by 3m rectangle.

The rest is tiled and surrounded by

wooden edging.

What length of edging is needed?

Work out the length of each side and add!

18m of edging is needed

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !

Picture It! ! Calculate It !

Read it !

6m

1.5m2m

4m

Problem 1Problem 1 The history classroom is 9m long The history classroom is 9m long

and 5m wide.and 5m wide.

How carpet is needed to cover the How carpet is needed to cover the floor?floor?

Problem 2Problem 2 The history classroom is The history classroom is 9m long and 5m wide.9m long and 5m wide.

How edging tape is needed How edging tape is needed for the carpet perimeter?for the carpet perimeter?

A length of 28m edging strip is needed

STEP 1

?

STEP 2

?

STEP 3

?

STEP 4

?Underline It !

Picture It! ! Calculate It !

Read it !

Problem 3Problem 3

The history classroom floor The history classroom floor is a 12m and 6m rectangle.is a 12m and 6m rectangle.

The resource corner is 2m The resource corner is 2m x 2m square. How much x 2m square. How much floor space is still free?floor space is still free?

Problem 4Problem 4

The history classroom floor is a The history classroom floor is a 12m by 6m rectangle.12m by 6m rectangle.

The resource corner is 2m x The resource corner is 2m x 2m square. A tiled border 2m square. A tiled border

marks the perimeter of the marks the perimeter of the remaining floor. How long is remaining floor. How long is

the border?the border?

An area of 68m² carpet is needed

Problem 6Problem 6What length of skirting What length of skirting

board is needed this board is needed this classroom?classroom?

(Remember to allow for the door!)(Remember to allow for the door!)KEY

Door

(0.5m wide)

15m

7m 6m

11m

43.5m of skirting board is needed.

Problem 7Problem 7How much floor space is How much floor space is there in this classroom? there in this classroom?

KEY

Door (1/2 m wide)

10m

7m5.5m

8m

The floor area is 59m²