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ACKNOWLEDGEMENT
First and foremost, I would like to thank God for He has given me strength and
patience to finish this project. I also would like to thank my Additional Mathematics teacher,
Madame Goh Siew Kiew for contributing assistance during the time being. I very much
appreciate the help she has given as well as the connection she has shared with me.
Moreover, a big thank you to my mother and father for giving the support I needed in
completing this project and for sacrificing their money, energy and time.
I also would like to express my highest gratitude to my friend, Ain Qistina binti Rosdi
for helping me during this project. Without these people, it would be possible for me to finish
this project.
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OBJECTIVE
1. Apply and adapt a variety of problem solving strategies to solve routine and non
routine problems
2. Experience classroom environments :
which are challenging , interesting and meaningful and hence improve their
thinking skills
where knowledge and skills are applied in meaningful ways in solving real life
problems
where expressing mathematical thinking , reasoning and communication are
highly encouraged and expected
that stimulates and enhances effective learning
3. Acquire mathematical communication through oral and writing and to use the
language of mathematics to express mathematical ideas correctly and precisely
4. Increase interest and confidence as well as enhance acquisition of mathematical
knowledge and skills through application of various strategies of problem solving
5. Develop knowledge and skills that are useful for career and future undertakings
6. Realize that mathematics is an important and powerful tool in solving real life
problems and hence develop positive attitude towards mathematics
7. Train themselves not only to be independent learners but also to collaborate , to
cooperate and to share knowledge in an engaging and healthy environment
8. Use technology especially the ICT appropriately and effectively
9. Train themselves to appreciate the intrinsic values of mathematics and to become
more creative and innovative
10.Realize the importance and beauty of mathematics
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INTRODUCTION
Polygon
A closed plane figure made up of several line segments that are joined together. The sides do not cross
each other. Exactly two sides meet at every vertex.
some polygons of different kinds
Types of polygon
Regular - all angles are equal and all sides are the same length. Regular polygons are both
equiangular and equilateral.
Equiangular - all angles are equal.
Equilateral - all sides are the same length.
Convex - a straight line drawn through a convex polygon crosses at most two
sides. Every interior angle is less than 180.
Concave - you can draw at least one straight line through a concave polygon
that crossesmore than two sides. At least one interior angle is more than
180.
Special Polygons
Special Quadrilateralssquare, rhombus, parallelogram, rectangle, and the trapezoid.
Special Triangles - right, equilateral, isosceles, scalene, acute, obtuse.
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Parts of polygon
Side - one of the line segments that make up the
polygon.
Vertex - point where two sides meet. Two or more ofthese points are called vertices.
Diagonal - a line connecting two vertices that isn't a
side.
Interior Angle - Angle formed by two adjacent sides
inside the polygon.
Exterior Angle - Angle formed by two adjacent
sides outside the polygon.
Names of polygon
Generally accepted names
Sides Name
n N-gon
3 Triangle
4 Quadrilateral5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
10 Decagon
12 Dodecagon
Names for other polygons have been proposed.
Sides Name
9 Nonagon, Enneagon
11 Undecagon, Hendecagon
13 Tridecagon, Triskaidecagon14 Tetradecagon, Tetrakaidecagon
15 Pentadecagon, Pentakaidecagon
16 Hexadecagon, Hexakaidecagon
17 Heptadecagon, Heptakaidecagon
18 Octadecagon, Octakaidecagon
19 Enneadecagon, Enneakaidecagon
20 Icosagon
30 Triacontagon40 Tetracontagon
50 Pentacontagon
60 Hexacontagon
70 Heptacontagon
80 Octacontagon
90 Enneacontagon
100 Hectogon, Hecatontagon
1,000 Chiliagon10,000 Myriagon
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Sandbox based on a polygon shape (hexagon)
Road sign based on a polygon shape (square)
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House based on polygon shapes
Ceiling lamps based on polygon shapes
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The definition of polygon is a plane figure with at least three straight sides and angles
and typically five or more. Polygons have been known since ancient times. The regular
polygons were known to the ancient Greeks, and the pentagram, a non-convex regular
polygon (star polygon), appears on the vase of Aristophonus, Caere, dated to the 7th century
B.C. Non-convex polygons in general were not systematically studied until the 14th century
by Thomas Bredwardine.
In 1952, Shephard generalized the idea of polygons to the complex plane where each
real dimension is accompanied by an imaginary one to create complex polygons. Surveyors
use them in mapping land every day. Engineers use them for calculating force distribution.
Painters use them for calculating the area of coverage they are going to be painting. They
actually are used quite a bit in everyday life. Things like calculating the square footage of our
home for insurance purposes, the square footage of a room for carpeting, the area of a yard
for being sodded all will require the use of polygons. Any time we are calculating area we
working with polygons.
http://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Complex_polytopehttp://en.wikipedia.org/wiki/Complex_polytopehttp://en.wikipedia.org/wiki/Star_polygonhttp://en.wikipedia.org/wiki/Pentagramhttp://en.wikipedia.org/wiki/Regular_polygonhttp://en.wikipedia.org/wiki/Regular_polygon7/31/2019 Addmath Ateh New
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(b) There are four other methods finding the area of a triangle:
1) base x height
2 ) ab sin C
3 ) where semiperimeter is a half of the triangles perimeter
s = (a + b + c )
4 )
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PART 2
(a)The cost needed to fence the herb garden
300 m x RM 20.00
= RM 6000
(b)
p m q m
q
100 m
To find area, use
To find , use Cosine Rule:
Rearrange,
( )
[ ]
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P (m) q (m) (degree) Area ()50 150 0 0
55 145 28.25 1887.46
60 140 38.21 2598.0665 135 44.81 3092.33
70 130 49.58 3464.10
75 125 53.13 3750
80 120 55.77 3968.63
85 115 57.68 4130.68
90 110 58.99 4242.64
95 105 59.75 4308.42
100 100 60.00 4330.13
Table 1
(c) Based on Table 1, the diameter of the herb garden so that the enclosed area is maximum
when the value of p and q is 100 m and the value of is 60.
(d) (i) Only certain values of p and q are applicable in this case, determine the range between
them.
By comparing,
| |
cos 1
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(ii) By comparing the length of p,q and the given side, determine the relation between
them.
p + q +100m = 300m
p + q = 200m
(iii) Triangle Inequality Theorem
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle
must be greater than the the measure of the third side.
Otherwise, you cannot create a triangle from the 3 sides.
This rule must be satisfied for all 3 permutations of the sides. In other words, as soon
as you know that the sum of 2 sides is less than the measure of a third side, then you
know that the sides do not make up a triangle.
b
c b
a
a
In the figure, the following inequalities hold.
a + b > c
a + c > b
b + c > a
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PART 3
(a)5 various other shapes of the garden that can be constructed so that the enclosed area
is maximum:
DECAGON
Knowing that,
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The formulae require:
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HEXAGON
6 = 360
Knowing that all of degree and length of each sides are same. Therefore,
The formula require:
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DODECAGON
Knowing that,
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The formulae require:
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OCTAGON
Knowing that,
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The formulae require:
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TRAPEZOID
The formulae require:
Where a and b are the lengthsof the parallel sides, and h is the height
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(b)(i) Three types of local herbs with heir scientific names that the farmer can plant in
the herb garden to meet the demand are :
Ginger Flower
(Etlingera elatior)
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Etlingera elatior (also known as Torch Ginger, Ginger Flower) is a species of herbaceous
perennial plant. Botanical synonyms includeNicolaia elatior, Phaeomeria magnifica,
Nicolaia speciosa, Phaeomeria speciosa,Alpinia elatior,Alpinia magnifica.
It is known in Malay as bunga kantan and it it eaten in a kind of salad preparation. The showy
pink flowers are used in decorative arrangements while the flower buds are an important
ingredient in dishes. Ginger flower is the soul of many Nyonya dishes such as the asam laksa,
Nyonya fish stew and curry dishes such as perut ikan and gulai tumis. More importantly the ripe
seed pods, which are packed with small black seeds, are an essential ingredient of the Karo
version ofsayur asam, and are particularly suited to cooking fresh fish.
Leaves ofE.elatiorhave the highest antioxidant, antibacterial and tyrosinase inhibition
activities among fiveEtlingera species studied. Antioxidant properties (AOP) of leaves were
significantly stronger than flowers and rhizomes. Leaves of highland populations had higher
AOP values than lowland counterparts. Thermal drying of leaves led to drastic declines in
AOP while freeze-dried leaves showed significant higher AOP values. Ethanolic extracts of
inflorescences have antimicrobial activity and are cytotoxic to HeLa cells.Antioxidant
activity of diarylheptanoids isolated from rhizomes is greater than -tocopherol.E.elatiorhas
an antioxidant effect against lead-induced hepatotoxicity in rats.
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Vietnamese coriander
(Persicaria odorata)
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Persicaria odorata, the Vietnamese coriander, is herbs which leaves are used in Southeast
Asian cooking. Other English names for the herb are Vietnamese mint, Vietnamese cilantro,
Cambodian mint and hot mint. In Malaysia and Singapore, it is called daun kesom or daun
laksa(laksa leaf). The shredded leaf is an essential ingredient of laksa, a spicy soup, so
much so that the Malay called it as daun laksa which means laksa leaf. It is not related to
the mints, nor is it in the mint family Lamiaceae but the general appearance and odor are
reminiscent. Persicaria odorata is in the family Polygonaceae, collectively known as
smartweeds or pinkweeds.
The Vietnamese coriander is a perennial plant that grows best in tropical and subtropical
zones in warm and damp conditions. In advantageous conditions, it can grow up to 15 to
30 cm. In the winter or when the temperature is too high, it can wither. The top of its leaf is
dark green, with chestnut-colored spots while the leaf's bottom is burgundy red. The stem is
jointed at each leaf.
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Ulam Raja
(Cosmos caudatus)
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Ulam raja, literally meaning "the Kings salad", was brought by the Spaniards from Latin America,
via the Philipphines to the rest of Southeast Asia. Ulam, a Malay word used to describe a preparation
that combines food, medicine and beauty is the widely popular Malay herbal salad. As a Malaysian
delight, it is served throughout the country from major hotels for tourists to buffet lunches or dinners
for the locals. The Malay people believe that the herb is good for health and contains anti-aging
properties or awet muda, and that it tones up blood circulation, strengthens the bones and promotes
fresh breath. The Malay people believe that the herb is good for health and contains anti-aging
properties or awet muda, and that it tones up blood circulation, strengthens the bones and
promotes fresh breath.
Ulam Raja is an annual plant growing up 2 m in height. The leaves are soft and pungent
while the stem is light green with a purplish hue and succulent. As night falls the leaves fold
to close the terminal buds as the plant literally sleeps. The flowers can be found solitary or in
a loose clusters and are produced on a single stalk on auxiliary heads.
It contains 0.3 percent protein, 0.4 percent fat and carbohydrates, it is also rich in laksium and
vitamin A. . The leaves are soft and pungent while the stem is light green with a purplish hue
and succulent. As night falls the leaves fold to close the terminal buds as the plant literally
sleeps. The flowers can be found solitary or in a loose clusters and are produced on a single
stalk on auxiliary heads.
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(ii) This is the logo that I have designed for the packaging of my herbs product that will play
an important role in attracting customers. I also have included a polygon shape in my logo.
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FURTHER INVESTIGATION
o Square is a regular quadrilateral.
o Rectangle is a irregular polygon.o The formula of area square and rectangle are the same :
o o Area of square is bigger than area of rectangle.
Let A be the area :
Square : o
oThe base and height of the square has the same amount since the sides are equal.
Rectangle :
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CONCLUSION
I have done researches and Ive been exchanging information with my friends
throughout this project. On completing this project, I have learned many important skills and
techniques. This project really helped me to understand more about the importance of
additional mathematics in our daily life . This project also exposed the applications of
additional mathematics in real life situations and the techniques of it. While conducting this
project, I have gained knowledge and wisdom.
Furthermore, this project encourages students to work together and in a team as we
human beings depend on each other. It also encourages students to gather information from
the internet and help students to improve their thinking skills. Last but not least, I propose
this project to be continued in the future because it certainly has promote effective
communication and mathematical skills to students.
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REFLECTION
In the process of conducting this project, I have learnt that perseverance pays off especially
the feeling of relief after completing the whole projet. For me succeeding in completing this
project has been a reward itself. I have also learnt that mathematics is essential in life because
our daily life depends on it according to the fact that even from the most simple things like
designing or constructing a garden, we must depend on mathematics. Besides that, I have
learned many moral values throughout finishing this project. In solving and finishing this
project, many techniques have been used in order to succeed:
Communication
Discussions with my teacher and friends helps me in solving problems. The
information from those discussions were being used as a reference material to
complete this project.
Reference
Additional of information from various of reference material helped me to find the
method to solve problems. For this Additional Mathematics project , Ive got
references from many sources.
Lesson session
Additional Mathematics lessons in class helped me a lot in solving problems by using
a certain equation that Ive learned in class.
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REFERENCE
http://en.wikipedia.org/wiki/Polygon
http://en.wikipedia.org/wiki/Triangle_inequality
http://www.mathsisfun.com/geometry/polygons.html
http://www.makcikbecok.org/2011/01/jenis-jenis-pokok-herba-dijadikan-ubat.html
http://www.herbamalaysia.com/
http://en.wikipedia.org/wiki/File:Assorted_polygons.svg
http://www.math.com/tables/geometry/polygons.htm
https://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/
webquest/webquest.htm
http://en.wikipedia.org/wiki/Ulam_raja_%28Cosmos_caudatus%29
http://en.wikipedia.org/wiki/Persicaria_odorata
http://en.wikipedia.org/wiki/Etlingera_elatior
http://www.dummies.com/how-to/content/geometry-formulas-for-polygons.html
http://www.onlinemathlearning.com/areas-of-polygons.html
http://www.picsearch.com/pictures/plants/herbs%20and%20spices.html
http://en.wikipedia.org/wiki/Polygonhttp://en.wikipedia.org/wiki/Triangle_inequalityhttp://www.mathsisfun.com/geometry/polygons.htmlhttp://www.makcikbecok.org/2011/01/jenis-jenis-pokok-herba-dijadikan-ubat.htmlhttp://www.herbamalaysia.com/http://en.wikipedia.org/wiki/File:Assorted_polygons.svghttp://www.math.com/tables/geometry/polygons.htmhttps://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/webquest/webquest.htmhttps://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/webquest/webquest.htmhttps://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/webquest/webquest.htmhttps://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/webquest/webquest.htmhttp://en.wikipedia.org/wiki/Ulam_raja_%28Cosmos_caudatus%29http://en.wikipedia.org/wiki/Persicaria_odoratahttp://en.wikipedia.org/wiki/Etlingera_elatiorhttp://www.dummies.com/how-to/content/geometry-formulas-for-polygons.htmlhttp://www.onlinemathlearning.com/areas-of-polygons.htmlhttp://www.picsearch.com/pictures/plants/herbs%20and%20spices.htmlhttp://www.picsearch.com/pictures/plants/herbs%20and%20spices.htmlhttp://www.onlinemathlearning.com/areas-of-polygons.htmlhttp://www.dummies.com/how-to/content/geometry-formulas-for-polygons.htmlhttp://en.wikipedia.org/wiki/Etlingera_elatiorhttp://en.wikipedia.org/wiki/Persicaria_odoratahttp://en.wikipedia.org/wiki/Ulam_raja_%28Cosmos_caudatus%29https://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/webquest/webquest.htmhttps://www.msu.edu/user/martynju/capstone/coursework/CEP_812/website/CEP812/webquest/webquest.htmhttp://www.math.com/tables/geometry/polygons.htmhttp://en.wikipedia.org/wiki/File:Assorted_polygons.svghttp://www.herbamalaysia.com/http://www.makcikbecok.org/2011/01/jenis-jenis-pokok-herba-dijadikan-ubat.htmlhttp://www.mathsisfun.com/geometry/polygons.htmlhttp://en.wikipedia.org/wiki/Triangle_inequalityhttp://en.wikipedia.org/wiki/Polygon