<< Chapter < Page Chapter >> Page >

8. Calculate the area of each square.

9. What can you deduce from this exercise?

10. Deduction: Write out Pythagoras’ theorem in the space below by making use of the triangle that is provided.

11. Solve x in each of the following triangles:(You may make use of your calculator.)

11.3

1.4

12. Do the calculations to determine whether the following is a right-angled triangle or not:

12.1 Δ size 12{Δ} {} DEF with DE = 8 cm, EF = 10 cm, DF = 6 cm

13. AREA OF TRIANGLES

13.1 Construct rectangle ABCD with AB = 45 mm and AD = 25 mm on a sheet of paper and cut it out. Draw diagonal AC .

13.2 Calculate the area of rectangle ABCD .

13.3 Cut out Δ size 12{Δ} {} ABC . What is the area of Δ size 12{Δ} {} ABC ?Paste it here.

  • Area of Δ size 12{Δ} {} ABC = ................. mm²

13.4 Are you able to develop a formula for determining the area any triangle?

Write it here:

13.5 Calculate the area of Δ size 12{Δ} {} ABC .

13.6 In the figure SQ = 15 cm, QR = 7 cm and PR = 9 cm.

Important : Provide all necessary information on your sketch. Check to see what you may need to complete the instructions fully.

(a) Calculate the area of Δ size 12{Δ} {} PSQ (accurate to 2 decimals).

(b) Now calculate the area of Δ size 12{Δ} {} PSR . Suggestion : You will first have to calculate the area of another triangle.

13.7 Calculate the area of ABCD .

14. Calculate the length of the unknown sides of each of the following:

14.1

14.2

14.3

15. Playing in a park is a necessary aspect of the development of a child.

  • You have been asked to supply slides. The problem that is involved requires calculating the length of the poles that are needed. Make use of the knowledge that you have accumulated to supply a plan to erect the slides.

The following is required:

15.1 a sketch

15.2 a scale, e.g. 1 cm = 1 m

15.3 Calculations must be completed fully.

Assessment

LO 3
Space and Shape (Geometry)The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.
We know this when the learner:
3.2 in context that include those that may be used to build awareness of social, cultural and environmental issues, describes and classifies geometric figures and solids in terms of properties, including:
3.2.1 sides, angles and diagonals and their inter­relationships, with focus on triangles and quadrilaterals (e.g. types of triangles and quadrilaterals).
LO4
MeasurementThe learner will be able to use appropriate measuring units, instruments and formulae in a variety of contexts.
We know this when the learner:
4.2 solves problems involving:
4.2.1 length;
4.2.2 perimeter and area of polygonals and circles;
4.3 solves problems using a range of strategies including:
4.3.1 estimating;
4.3.2 calculating to at least two decimal positions;
4.3.3 using and converting between appropriate SI units;
4.4 describes the meaning of and uses π size 12{π} {} in calculations involving circles and discusses its historical development in measurement;
4.5 calculates, by selecting and using appropriate formulae:
4.5.1 perimeter of polygons and circles;
4.5.2 area of triangles, rectangles circles and polygons by decomposition into triangles and rectangles;
  • investigates (alone and / or as a member of a group or team) the relationship between the sides of a right-angled triangle to develop the Theorem of Pythagoras;
4.9 uses the Theorem of Pythagoras to calculate a missing length in a right-angled triangle leaving irrational answers in surd form (√);
4.10 describes and illustrates ways of measuring in different cultures throughout history (e.g. determining right angles using knotted string leading to the Theorem of Pythagoras).

Memorandum

ACTIVITY 1

1.1 a) all 3 Acute-angled

b) one 90 o angled

c) one obtuse-angled

1.2 a) 2 even sides

b) 3 even sides

c) sides differ in length

2. The sum of the interior angles of any triangle is 180º

ACTIVITY 2

10. r 2 = p 2 + q 2

  • x 2 = 12 2 + 5 2

= 144 + 25

= 169

size 12{∴} {} x = 13

  • 20 2 = 8 2 + x 2

x 2 = 400 – 64

= 336

size 12{∴} {} x size 12{ approx } {} 18,3 cm

11.3 size 12{ nabla } {} ABC : x 2 = 70 2 – 29 2

= 4 900 – 841

= 4 059

size 12{∴} {} x size 12{ approx } {} 63,7 mm

11.4 y 2 = 4 2 + 3 2

= 16 + 9

= 25

size 12{∴} {} x size 12{ approx } {} 9,4cm

12. DE 2 + DF 2 = 100 = EF 2

size 12{∴} {} DEF right angled

(Pythagoras)

  • ½ x b x h
  • BC 2 = 13 2 – 5 2

= 169 – 25

= 144

size 12{∴} {} BC = 12 cm

Area ABC = ½ x b x h

= ½ x 12 x 5

= 30cm 2

13.6 (a) PS 2 = 9 2 – 8 2

= 81 – 64

= 17

size 12{∴} {} PS = 4,12 cm

Area PSQ = ½ x b x h

= ½ x 15 x 4,12

= 30,9cm 2

13.6 ( b ) Area PSR = ½ x 8 x 4,12

= 16,4 cm 2

Area PRQ = area PSQ PSR

= 30,9 – 16,4

= 14,5 cm 2

13.7 AC 2 = 12 2 + 8 2

= 208

size 12{∴} {} AC size 12{ approx } {} 14,4

AD 2 = 16 2 – 14,4 2

= 256 – 207,36

= 48,64

size 12{∴} {} AD = 6,97

Area ABCD = area ABC + area ACD

= (½ x 12 x 8) + (6,97 x 14,4 x ½)

= 48 + 50,18

= 98,18 square units

  • a 2 = 8 2 – 7 2

= 15

size 12{∴} {} a size 12{ approx } {} 3,9

b 2 = (3,9) 2 + 4 2

= 15,21 + 16

= 31,21

size 12{∴} {} b size 12{ approx } {} 5,6

  • x = 18 (radius)

y 2 = 36 2 – 13 2

= 1 296 – 169

= 1 127

size 12{∴} {} y = 33,6

  • UV 2 = 12 2 – 7 2

= 95

size 12{∴} {} UV = 9,8

VS 2 = 14 2 + ( size 12{ approx } {} 9,8) 2

= 196 + 95

= 291

size 12{∴} {} VS = 17,1

y 2 = ( size 12{ approx } {} 17,1) 2 + 5 2

= 291 + 25

= 316

size 12{∴} {} y = 17,8

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Mathematics grade 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11034/1.1
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Mathematics grade 8' conversation and receive update notifications?

Ask