ADDITIONAL MATHEMATICS PROJECT WORK

1/2012

NAME: MUHAMMAD FIKRI BIN ABDUL HALIM

CLASS: 5 IKHLAS

NRIC:

TEACHER: ENCIK HALLID BIN BARI

SCHOOL: SAMT TENGKU AMPUAN JEMAAH, SEKSYEN 11 SHAH ALAM, SELANGOR

OBJECTIVESThe aims of carrying out this project work are:

I. To apply and adapt a variety of problem-solving strategies to solve problems

II. To improve thinking skills

III. To promote effective mathematical communication

IV. To develop mathematical knowledge through problem solving in a way that increases students’ interest and confidence

V. To use the language of mathematics to express mathematical ideas precisely

VI. To provide learning environment that stimulates and enhances effective learning

VII. To develop positive attitude towards mathematics

ACKNOWLEDGEMENTFirst and foremost, I would like to thank Allah that finally, I have succeeded in finishing this project work. I would like to thank my beloved Additional Mathematics teacher, En Hallid bin Bari for all the guidance she had provided me during the process in finishing this project work. I also appreciate his patience in guiding me completing this project work. I would like to give thousand thanks to my parent for giving me their full support in this project work, financially and mentally. I would also like to thanks my friends who had helped me in finding the information that I’m clueless of, and the time we spent together in study.

CONTENTS NO CONTENT PAGE

1 OBJECTIVES

2 ACKNOWLEDGEMENT

3 INTRODUCTION

4 PART 1

Part 1 (a) Part 1 (b) Part 1 (c)

5 PART 2

Part 2 (a) Part 2 (b) Part 2 (c) Part 2 (d)(i) Part 2 (d)(ii) Part 2 (d)(iii)

6 PART 3

Part 3 (a) Part 3 (b)(i) Part 3 (b)(ii)

7 REFLECTION

8 REFERENCES

INTRODUCTION

A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments (i.e., by aclosed polygonal chain). These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices(singular: vertex) or corners. An n-gon is a polygon with n sides. The interior of the polygon is sometimes called its body. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions.

The word "polygon" derives from the Greek πολύς (polús) "much", "many" and γωνία (gōnía) "corner" or "angle". (The word γόνυ gónu, with a short o, is unrelated and means "knee".) Today a polygon is more usually understood in terms of sides.

The basic geometrical notion has been adapted in various ways to suit particular purposes. Mathematicians are often concerned only with the closed polygonal chain and with simple polygons which do not self-intersect, and may define a polygon accordingly. Geometrically two edges meeting at a corner are required to form an angle that is not straight (180°); otherwise, the line segments will be considered parts of a single edge – however mathematically, such corners may sometimes be allowed. In fields relating to computation, the term polygon has taken on a slightly altered meaning derived from the way the shape is stored and manipulated in computer graphics (image generation).

Polygons have been known since ancient times. Theregular 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 Bradwardine.

In 1952, Geoffrey Colin Shephard generalized the idea of polygons to the complex plane, where each real dimension is accompanied by an imaginary one, to create complex polygons.

PART 1

a)

b) Definition and History of Polygon:

Polygon is defined as a closed, 2-dimensional shape made up of three or more straight line segments connected end to end to end.

History:

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.

c) The four different methods of finding the area of a triangle is stated below:

Method 1:

h

bIf you know base (b) and height (h) of the triangle, the following formula can be applied.Area = ½ x b x h

Method 2: a c

bIf you know three sides (a, b and c) of the triangle, Heron’s Method can be applied. s = (a+b+c) / 2Area = s (s-a) (s-b) (s-c)

Method 3: a bIf you know two sides (a and b) and the included angle (), the following formula can be applied.Area = ½ x a x b x sin

Method 4:

If you know coordinate of the three vertices, the following formula can be applied.

= ½ (x1y2 + x2y3 + x3y1 – x2y1 – x3y2 – x1y3)

Method 5:

If you know equation (y=mx+c) of the three lines, integration can be applied.

Area = (mx1 + c) dx + (mx2 + c) dx - (mx3 + c) dx

PART 2

a) Cost needed to fence the herb garden = RM20.00 per metre x 300m= RM6000.00

b) Table attached together at back.

c) In order for the enclosed area to be maximum around 4330.13m2, the shape of the triangle must be equilateral. Therefore, the length of both p and q must be 100m.

d) (i) 50<p<150 and 50<q<150

(ii) p α 1/q

b

A C

c a

B

(iii) A2 = B2 + C2 – 2 x B x C x cos (a). This theorem is known as ‘Cosine Rule’.

PART 3

a) (i) Quadrilateral 2x + 2y = 300m2

x + y = 150m2

y m Area= xy

x m

x y Area= xy10 140 140020 130 260030 120 360040 110 440050 100 500060 90 540070 80 560075 75 5625

The maximum area is 5625m2

(ii) Regular Pentagon

5a = 300

a = 60

tan54°=t/30

t = 30 tan 54° = 41.2915m

Area = ½ (41.2915 x 60) x 5 = 6193.73m2

a

a

a

a

a

(iii) Semicircle

2 r+πr=300

r= 3002+π

Area=12 ( 300

2+π )2

π=5347.55 m2

(iv) Circle

2 πr=300

r=150π

Area=12 ( 150

π )2

(2π )=7161.97 m

(v) Hexagon

6 a=300

a=500

Area=12

x50 x50 x sin60 ° x6=6495.19 m2

Conclusion:

Circle is the best among the other shapes. It gives maximum enclosed area.

2 πr=300

r=150π

Area=12 ( 150

π )2

(2π )=7161.97 m

b) (i)

Lemon Grass - (Cymbopogon flexuosus), also called Cochin Grass or Malabar Grass (Malayalam: ഇഞ്ചി�പ്പു�ല്ല്�(inchippullu), is native to Cambodia, India, Sri Lanka, Burma,and Thailand while the West-Indian lemon grass(Cymbopogon citratus), also known as serai in Malay, is assumed to have its origins in Malaysia. Indonesian people used to called it serai too or sereh. While both can be used interchangeably, C. citratus is more suited for cooking. In India C. citratus is used both as a medical herb and in perfumes. Cymbopogon citratus is consumed as a tea for anxiety in Brazilian folk medicine, but a study in humans found no effect. The tea caused a recurrence of contact dermatitis in one case.

Orthosiphon stamineus ( Misai Kucing ) - is a traditional herb that is widely grown in tropical areas. The two general species, Orthosiphon stamineus "purple" and Orthosiphon stamineus "white" are traditionally used to treat diabetes, kidney and urinary disorders,high blood pressure and bone or muscular pain.

Tongkat Ali - It has become popular for its testosterone-enhancing properties. Because of that, it is included in certain herbal supplements for bodybuilders. Historically, it has been used by the folk medicine in its countries of origin as a libido enhancer and to treat various sexual dysfunctions. Numerous scientific studies performed by Malaysian Universities, including University Science Malaysia (USM) have confirmed its effects on enhancing sexual characteristics in animal models. Currently, it is being researched for its possibilities as an anti-cancer supplement.

REFLECTIONWhile I conducting this project, a lot of information that I found. I have learnt the uses of

polygons. I also learned some moral values that I practice. This project had taught me to be responsible on the works that are given to me to be completed. This project also made me felt more confidence to do works and not to give up easily when we could not find the solution for the question. I also learned to be more discipline on time, which I was given about three weeks to complete these project and pass up to my teacher just in time. I also enjoyed doing this project during my school holiday as I spent my time with friends to complete this project and it had tighten our friendship.

REFERENCES

http://en.wikipedia.org/wiki/Polygon

http://www.scribd.com