Pupil Work Booklet - ftnSUOe-T SMaths

Week commencing 30/03/2020

Work to be completed

D Wednesday 1st April - Area of parallelogramsD Thursday 2nd April - Area of trianglesD Friday 3rd April - Further work on the area of trianglesD Monday 6th April - Area of compound shapesD Tuesday 7th April - Reviewing area and perimeter

•

Resources / links to help with work:

D Resource for Work l - https://corbettmaths.com/2013/12/21/area-of-a-parallelogram-vicleo-44/D Resource for Work 2 and 3 - https://corbettmaths.com/2013/12/20/area-of-a-triangle-video-49/D Resource for Work 4 - https://corbettmaths.com/2012/08/02/area-of-compound-shapes/

Support:

These workbooks have been designed for you to work through them independently. There areseveral support resources available through the links above and further help inside this booklet.

However, if you have really tried but are still stuck or do not understand what is being asked,please email your form tutor with clear details of the subject, page number and question/issue thatyou have.

Why is the work in this booklet important to complete?

The maths work in this booklet covers perimeter and area - a key topic in mathematics as wellas the wider world. Many careers like architecture, aeronautical and graphics design, engineeringand many others include the use of area and perimeter on a regular basis. Furthermore, this topicis important for every individual for when they choose to remodel, buy, or decorate a new home tomake sure that they get the maximum use of their house.

1

Pupil timetable and Guidance

Each day you are expected to be working on each subject for 20 mui each weekday

It may be that it is not always possible. If this is the case, then you must try to make up the timewhen you can.

Where should I do my work?

You should find a place where you can do focused work without distractions e.g. phones, TVs, gamesconsoles nearbyIt's a great idea to get someone to take these distractions away from you so that you can do yourwork.

How should I do my work?

All work should be written up in your 'Workbook' that you were given. You need to write the subjectbefore the title and then the way you layout this book is exactly the same as you would in lesson witheach page having a title and date.All work should be done to the best of your ability and show that you are aiming high ansdmodelling determination.

What if I get stuck or don't understand?

If you don't understand or get stuck you will find a number of help points in your booklets such assentence starters, links to online resources such as YouTube clips or BBC Bitesize revisionIf you are still stuck, then you can email your form teacher or ask your parent/guardian to emailthem for help make sure you let them know very clearly what it is you do not understand. Thisincludes details of the subject, page number and the issues you have.

How do I know if I am right?

Inside the booklet you will find points to test yourself and some answers. You can also find out if youare correct by using the additional support resources such as the linked video clips and reading

What if I finish aU my work?

If you finish your work, you should quiz yourself so that learning sticks in your long-term memory.Each booklet also has stretch questions which should be completed and an optional homeworkproject which can also be doneWe very strongly recommend that you use this time to read a mixture of fiction and non-fictionbooks.

2

Work 1 -Area of paralleloarams

|The base of a parallelogram and the height of a parallelogram are perpendicular.|This means they meet at a right angle.

height/

/

/- - - -

base

height

base

When you cut and move the triangle to the other side, you have ns>t changed theshape's overall area. Therefore, the parallelogram and the rectangle have the samearea.

To work out the area of a parallelogram, you therefore multiply the base by the heightjust like you would for a rectangle.

Important:10cm

lu

5cm^6cm

The labelled position of the base and height on your diagram may change.Always look out for the perpendicular lengths.

In the diagram above, the base is 10cm and the height is 5cm.

The slanted length labelled 6cm is neither the base nor the height and is notrelevant to working out the shape's area.

In this case, to work out the area we multiply 10 by 5 and get an area of 50cm2.

But to work out its perimeter: 10+ 10+6+6= 32cm

3

Copy and complete the sentences:

Concept Corner

The area of a parallelogram is equivalent to the area

of a f'^^^^fiLwith the same width and ( -^ p <T'JiCUtCir]heightWe can show this by cutting and rearranging aparallelogram to construct a rectangle.

f--------)rectangle i

<>--------/f--------)1 perpendicular »^--------/^---—----^

-> //

Answer the following questions:1. The following parallelograms are drawn on centimetre-squared paper. Find the

area of each.

(a) (b) (c)2.

A =20cw'Scm

4c^lcw\ ;3cm'

II

4crY)

f\ - gc^lCfYl

(\= Gcmz

2. Calculate the areas of the parallelograms below. Include suitable units.(a) (b) fc1

-^—^ • -^—»—< 12cm..2cm 4cm

-»-8cm

A ^ I fccw'. \ \\

(d) (e)fi'l^i

^ ZT7: 8cm

R^ ^Gcw1(0

\\

5cm

—^-'6^

,9cm 1A - 4.^~ c,m'fe) "r^-

5m <1

(h)

r 2.8m ^

^\\ 4.5cm 21mm'\ " \^ft.i8c4cn?L ft-^-To^.v-

63.5cm ^ 9^(0

50cm

A -l4-mz

^

6̂

1.2m := (20 cr^

90cm

A ^aii-^cYYi2" pi^io,s>oocmLo^(•osml~.

4

STRETCH:

Construct the following parallelograms using a ruler and protractor.Find their area by measuring the appropriate lengths.

</

4.7 cm /', @1^,

68°

5cm

A

4.5 cm;

t

4

©1050

V:N4.2 cift>

A

6.3 cm /

12

@y

^L^<-' 6.3 cm

Not to scale

&^ n^^ Pa^e. —^

5

0

(D-*

A

<F 4.3cm0

^s

^3^

c ,ft 2a

(o8

S~^ro\

I

/;'

;r

,r

/'•",."

-^<f'

rf-"

\

Aft(x--5~^l+-3)

^ 2> ^cfhz-

/

/

L+.SC^4cm,

—>

005

4-1cm

f\^(^ r 4 ^ >- ^

i^cpn

er/z'

^0

^)^

^(o8t}

4nv.

I^•6cr^

G3cr^ .

^.l .

Afejx^

^•.G ?<.fc ^^>

^ 3S~-2^c<v\1'-

t

\,,

Work 2 - Area of trianales

We can find the area of a triangle using its base and perpendicular height andcomparing it to a rectangle with the same dimensions.

height

base(

|!1

base

I

heig ht heightl

base base

Each of the triangles above have the same base and perpendicular height as therectangle drawn around them.Each triangle takes up exactly half the amount of space as the rectangle.As a result each triangle's area is half the area of the rectangle with the samebase and perpendicular height.Each rectangle's area is 18 square units, so each triangle's area is 9 square units.

Example:

Calculate the area of the triangle below:

4cm7.2cm

6cm

4cm7.2cm

6cm

(not to scale]

The base is 6cm and the height is 4cm.

The rectangle with the same dimensionswill have an area of 4x 6 = 24cm2.

The triangle's area is exactly half of therectangle's area, so the triangle's area is 12cm2.

Calculations for the area of a triangle areoften written like this:

A^A = 12cm2

The 7.2cm length does not form the base northe height of the rectangle, so is not relevantwhen working out the triangle's area.It would be relevant, however, if you wantedto calculate the triangle's perimeter:

4+A +7.2= 17.2cm

6

Answer the following questions:1. Calculate the area of the triangles below that are drawn on centimetre-squared

paper, hlint: draw the rectangles around the triangles first.

b)6.15c

aj cl

3^ rr

4dml ,6.^4crtn

i 5dm8cnh

5ch

Al=l lOd.fY) T-I

S^rrj/brrti

ft - 20c^z A^tG-scmz

2. Calculate the area of the triangles below. Include suitable units.

a)

8cm10cm

6cmA=24cm'-

b)8cm

4cm

7cm

A = t4cm'

c)

12cm13cm

5cmA^30c^L

d]

6cr^

ft=ac^

4cm

9)27c

:25c

40cm

A ^^oocm'

e)

5cm2cm

14cmf\r 3^cr^

2-

h]

18m20m

4m

f\ ^ \^om

f) 9cm

3cm8c

ft--16 ^cy

i)

10cm 8c

t

12cmz.

ft r 48cm'-

7

STRETCH:1. Calculate the area of these two triangles

.L'-.. 5 cma) ^

3 <flcm

4 cm^

b)

¥

: 3cm

3.5 cirt.\

^ '^T—4"'""S cm

ft:b^L ."i^-c-m.1 ft ° 3^- -- ^•scw'~~^~ -~~~—"" 2

2.a) Construct the three triangles below.b) Find the areas of each triangle by measuring a base and a perpendicular height.

How many ways are there to find each triangle? Give your answer to 1 dp.

-T ••*-•ii)») --'

5.8 cm ---:\ .-

-•'.-'-, .'

.--6.5 cm *•- .< .--.-'

\ t.95 fc.-•\^3^--' 3 cm<'4vi-'

Hi)

/3.9 cm

-»4.5cm

6

.'

75

Not to scale

'^

^-'4.5 cm

SdQ. n^^ P^^

8

•/I

//

^

/\\

£.J

L/)<s>

0

^

3<^w

(b <ocn\. Pi = 2> .< <G'(o-2-

r C1 ^cfn2.

,'

,/'

A-- 2>-°\ ^ Lf5--L

E<^ s0^ <Ju

0-^ 0-

ro -0

•J'

4 s" cw

!

1.S'^-'^^TCVY\~ "

Ill

S-s~c^\

06?-^s

'^

ft<^a r ^'s' /. i+.s"2-

^ \Z-^~t-Scm2.

L^.S cm

Work 3 - Further work on the area of trianglesSometimes you can be asked to use the area of the triangle to work out either its heightor its base length.

Examples:

Qj The triangle below has an area of 24cm2. Calculate the length of b.

4cm

Whenever you know the area of a triangle, always then work out the area ofthe rectangle around it with the same height and base.

4cm

b

~! The area of the rectangle is always doublethe area of the triangle.

If the triangle's area is 24cm2, then the areaof the rectangle is 48cm2.

4cm 48cm2

b

4 multiplied by b must therefore make 48.

So we divide 48 by 4 in order to work out y.

48-4= 12y = 12cm

Qj The triangle below has an area of 40cm2. Calculate the length of h.

|h

8cmWhenever you know the area of a triangle, always then work out the area ofthe rectangle around it with the same height and base.

tha

8cm

h

I

h

80(^m2

1.8cm

The area of the rectangle is always doublethe area of the triangle.

If the triangle's area is 40cm2, then the areaof the rectangle is 80cm2.

h multiplied by 8 must therefore make 80.

So we divide 80 by 8 in order to work out h.

80-8= 10h = 10cm

9

Answer the following questions:1. The area of the triangle is 20cm2. Calculate the length of x. (Remember to first draw

the rectangle around the triangle and work out what the rectangle's area mustbe)

~^ x^ ^2.0

z

^c ^S" = 40

3c ^ ^crv)

x

5cm2. The area of the triangle is 30cm2. Calculate the length of y.

y A <o ^302

y Afc ^ GO

^ ^ ^ (Ocr^

6cm

y

3. The area of the triangle is 12cm2. Calculate the length of z.

^ x*° - ii-

z

i>. fc

~i

- 2t+

4cm

z

6cm

4. The area of the triangle is 56cm2. Calculate the length of a.

2^(\2-

- ST<o

^^c\

a =

^ nz

I^CKV)

8cm

a

5. The area of the triangle is 165cm2. Calculate the length of b.

t^^b ^ ^^-z

S-Ab ^

b^

15cm I

33>0

11cmb

10

Qj Calculate the area of this compound shape

7cm

7cm,

7cm

7cm

11cm

13cm

15cm

7cm,

11cm

(not to scale)

13cm

If you split the compound shape alongthe dotted line, it becomes a rectangleand a triangle.

15cm 7cm|7c

7c6cm

15cm

The base is the difference between 15cm and 11cm

The height is the difference between 13cm and 7cm4cm

15cm

The area of the rectangle is 7x 15 = 105cm2.

7c6cm

4cm

Area of a triangle: base x height2

Base = 4Height = 6

4x6=2424-2= 12

The area of the triangle is 12cm2.

The total area of the compound shape is 105 +12= 117cm2

12

Work 4 - Areas of compound shapes

Compound shapes are shapes that are made up of two or more simple shapes.To work out the total area of a compound shape:

1) Split it up into its simple parts;2) Calculate their separate areas;3) Add the separate areas all together.

Examples:

Q] Calculate the area of this compound shape

12cm

,9cm

|7cm

12cm

,9cm

8cm

If you split the compound shape along the dotted line,it becomes a rectangle and a triangle.

7cm

8cm

7cm

5cm

The height of the triangle ^^>^is the difference between

12cm and 7cm

8cm

9cm

8cmThe base of the triangleis the same as the baseof the rectangle

7cm

8cm

5cm9cm%//m

8cm

III

The area of the rectangle is 8x 7 = 56cm2

The area of the triangle is going to be half the area ofa rectangle with the same dimensions.

Area of a triangle: Base x height2

Base = 8cm

Height = 5cm(the 9cm is not relevant for working out the area]

Area of the rectangle is 40cm2, so the area of thetriangle is 40 -2 = 20cm2.

The total area of the compound shape is 56 + 20 = 76cm2

11

Answer the following questions:

1. Calculate the area of each compound shape

<oAic3 ^(a) _ ^'~3—. Cb)

3cm/

4^'^ =ZOcrn~'z

r <^CiW

fc^l+i.

24CM'8cm ^MQ

^ 80cm

<^

4-cy^'12cm

(c)

3cm

^^^

(

"X-

^...2>3~cm'

-;|0-S'C

A8cmI

I & cm

m2.

-^OLifM II I I ^ SV^n II I - o-"---' | |t>

A-14 t^ 6c3m>cm^ A-So4^cmtOocm'- ^3^+(S?-^^Ltd) ^S^-.ZQ^ te) ^cm_ ,.,^ JcrTL cf) /\ 6cm

-22mUsw^s—.

$^

20m 3>0 A I ^^-.4^0m'L ^

15mt

^IF"20cm

30m 32cm

Pi^ 4^0 + 20 ^ ^.TOm2' I\H(X^[ 1-orcLi ^c^^^ Six.'10 =(o^^m •

PtT^o(- cu^uh ^la^UL

(bP 4cm L

4cr £

n

@6cm

i^)^ ^ : izcm-z

STRETCH:Calculate the shaded area

^<^(\ 0^ ^VvtLt^OL9^VArvv •Q^G^^=tgw"1@^^-- ^'^,

^tU^Uf^^^ ^. . , .,^1C<S) -^ ^Lll -- ^c"'' (D 4 ^4- it 'm-

2.TO^TCL^ hYe^:

d}^^ -. ac^^

6,40-3^'=66fw~. 1

m

-f6^-OJL^^; ^1^ f<^ r Z^

P^V^aoj- \^^z [\Ho^e.3\u^^

^ct-a^^G-^iz^ ^lm .friarvs^ = G ^l1' -~ 3 £ rvi1'

2-

Toi-oji f\vfta ^ ^-'2-t2>^ ^ (O^m^

s"^

3

^

^3is

6 fim!g

© 3 6mm

^a6

< ^

-\-ov<^ ^^'iz^-lfc+t^-^o^1'

12m^^0l o(- &K<x^d ^OA:

f6S - 2-"^

^^lm^

13

Work 5 - Reviewing area and perimeter

Using all of your learning from this week and last week, answer the following questionsremembering to include your units in your final answers.

1. Work out the area and perimeter of the shape below that is drawn on a centimetre-squared grid.

J_

F\^a--lctcm1-P<iTi^e^r^ 2£cm .

2. Calculate the area and perimeter of the rectangle below.7cm

3cm

(\^(\= aicm-L

7cm

= 3^-^J

P^inf^iiteLr- 311 ^ 3> -t^

= 2-OCt^3. Shown below is a wooden picture frame. Work out the shaded area.

12cm

8cm

10cm

^no|- lo.rg& ^t^^-^ 11 ^lt4 -~ lfc^LH\~-

14cm (\^0<0(. SmOLL^ r^^^^^ ^^\o- go^r^'

ShacJbLd ^^ ^^ 16^-^0= <^lcw .

4. Calculate the area and perimeter of this compound rectilinear shape'^~c»r\

Not to scale ftT ^ r

9cm

s>^

^4^^^0

3cm

^> x 5I -Sc^z- 3cm

8cm

ci+4s:~ ^4-cm<L

Ptri'Y^^I-t^r^+s-4-G +S+3+s>

^2 4-^

14

5. Calculate the area and perimeter of this parallelogram

T

5cm : 4cmtL

Arza-- ^4^l'L

^ 4 -gcr^i.\

P^rjm^^r ^5-Ki t^-KL?34<-m

12cm

6. Calculate the area and perimeter of this right-angled triangle

ft^o^-- G^-Umz2.

Pdyim^r^l4.m

10m6m

8m

7. The triangle below has an area of 42cm2. Calculate the length of y.

y L^^^ ^ 47-<^z

fc. %^y^6cm

^ 11^ crv^

8. Calculate the area and perimeter of this compound shape

P^Y ^ '.

0(°?i^ 2icn

Co^ 20m±

2-

"^©^"s*

/^ 2.0^1 S "3&0rn2' llm

® 18m

•fo+o^ ^^^^ ^GO ^^-

-^ ^Slm^

14m

15

What can I do to aim even higher?

Using the internet, research how to calculate thearea of trapeziums and create a poster

explaining clearly how to do it.

Include diagrams, clear explanations andexample questions.

16