New formulas in area

Ahmed, Ehab Esmsail

doi:10.21608/ijsrsd.2018.8547

	New formulas in area
International Journal of Sustainable Development and Science
Article 9, Volume 1, Issue 2, June 2018, Page 1-9 PDF (814.53 K)
Document Type: Original Article
DOI: 10.21608/ijsrsd.2018.8547
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Author
Ehab Esmsail Ahmed
Cairo University
Abstract
This formula develops old theories to facilitate the solution The use of geometric spaces is very important in our live. In ancient times it took many steps to resolve the area of the triangle, but in this research, it will be easy to solve the area of triangle with one side and two angles only and this saves time , effort and thinking. In Old times, solving rhombus area took a number of difficult steps, but in this research it will be easily solved.. Generally, rhombus area is calculated by half multiplied the lengths of the two diagonals, but in but in this research area is calculated in terms of one diagonal length and an angle only Parallelogram area is equal to multiplication of the base length by the perpendicular , but the new method uses diagonal length and angles of the diagonal only Area of the rectangle equal multiplication of length and width, Using the new method diagonal length and angles of the diagonal are used only Uses 1- triangle area in a new method 2- parallelogram area a new method 3 – rectangle area in a new method 4 - rhombus area in a new method 5 - square area in a new method
Keywords
The area; Triangle; rhombus (diamond); Parallelogram; rectang


Full Text
New formulas in area Ehab esmail ahmed Bank el taslef Street, Tahta, Sohag, egypt mathehab75@yahoo.com E-mail Abstract This formula develops old theories to facilitate the solution The use of geometric spaces is very important in our live. In ancient times it took many steps to resolve the area of the triangle, but in this research, it will be easy to solve the area of triangle with one side and two angles only and this saves time , effort and thinking. In Old times, solving rhombus area took a number of difficult steps, but in this research it will be easily solved.. Generally, rhombus area is calculated by half multiplied the lengths of the two diagonals, but in but in this research area is calculated in terms of one diagonal length and an angle only Parallelogram area is equal to multiplication of the base length by the perpendicular , but the new method uses diagonal length and angles of the diagonal only Area of the rectangle equal multiplication of length and width, Using the new method diagonal length and angles of the diagonal are used only *Uses* 1- triangle area in a new method 2- parallelogram area a new method 3 – rectangle area in a new method 4 - rhombus area in a new method 5 - square area in a new method Keyword The area; Triangle; rhombus (diamond); Parallelogram; rectang الملخص عربى هذه الصیغ تطویر لنظریات قدیمة لتسهیل الحل استخدام المساحات الهندسیة هام جدا فى حیاتنا قدیما کان یستخدم خطوات کثیرة لحل المساحة للمثلث ولکن هذا البحث یسهل حل المثلث ومثال ذلک مساحة المثلث بضلع واحد فقط وزاویتین وذلک یوفر الوقت والجهد والتفکیر قدیما یتم حل مساحة المعین بطریق صعبة ولکن فى هذا البحث یتم الحل بسهولة مساحة المعین نصف حاصل ضرب القطرین ولکن فى القانون الجدید المساحة بدلالة قطر وزاویة فقط مساحة متوازى الاضلاع تساوى القاعدة فى الارتفاع ولکن القانون الجدید بدلالة قطر وزاویتى القطر فقط مساحة المستطیل تساوى الطول فى العرض ولکن القانون الجدید بدلالة قطر وزاویتى القطر فقط وبذلک یسهل الاجابة فى ایجاد مساحة المثلث والمعین والمستطیل والمربع بطرق جدیدة وهذا یفید الطلاب فى هندسة مدنى کلیة الهندسة Introduction Calculating the area of a triangle using the length of one side and two angles is better than using the old solution solving rhombus area took a number of difficult steps, but in this research it will be easily solved. Generally, rhombus area is calculated by half multiplied the lengths of the two diagonals, but in but in this research area is calculated in terms of one diagonal length and an angle only Parallelogram area is equal to multiplication of the base length by the perpendicular , but the new method uses diagonal length and angles of the diagonal only Area of the rectangle equal multiplication of length and width, Using the new method diagonal length and angles of the diagonal are used only *Idea of the research* "The new methods" The area of : (1) Triangle (2) rhombus (diamond) (3) Parallelogram (4) rectangle The area of triangle A b c Figure(6.1) ^proof the area of the triangle = × (a b)× (a c)× sin ȃ ⁰₀⁰ = 0⁰0 ac = (ab) × sin (b) / sin (c) ⁰₀⁰ sin c = sin(180- ( a + b )) = sin ( a + b ) from (1), (2), (3) ⁰₀⁰ The area at triangle = Example (1) c 2 cm 45 1cm 45 a 1 cm b Solution (1) The Area of triangle abc = a b × b c × sin b = × 1 × 1 × 1 = cm² Solution (2) by new method The Area of triangle abc = = = = cm² Example (1) a 30 5 cm 70 b c The Area oF abc = = = 5.96 cm² The area of parallelogram d c 3 2 a b Figure (6.2) The proof The area of parallelogram a b c d = 2 × area abd = 2 × ⁰₀⁰ ab // bc 0⁰0 m ( 3 ) = m ( 1 ) from (1) , (2) 0⁰0 area a b c d = ^\ example (1) a b 5 cm 40 30 d c Area of a b c d = = 8.55 cm² The area of rhombus (diamond) b a c 2 1 d Figure (6.3) ^Proof ⁰₀⁰ Area of a b c d = ⁰₀⁰ m(1) = m(2) = m( from (1), (2) ⁰₀⁰ Area of a b c d = new method example b a 4 cm c 30 30 d Area of a b c d = = = = cm² (2.4)The area of rectangle ^{a b} ^{1 2} ^{d c} Figure (6.1) ^Proof ⁼ = (bd)²× sin(2) cos(2) Because sin(90) = 1 Sin (1) = cos(2) because 1+2 = 90 References Book calculate areas and volumes of geometric shapes Carson, P. B. (2012). Effects of levels of formal educational training in mathematics on teacher self-efficacy (Doctoral dissertation, Piedmont College).‏ Gardner, R. J. (1995). Geometric tomography (Vol. 1). Cambridge: Cambridge University Press http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-triangleformulae-2009-1.pdf httpfiles.books.elebda3.netdownload-pdf-ebooks.org-ku-9199.pdfhttp://www.mathcentre.ac.uk/resources/uploaded/mc-ty-triangleformulae-2009-1.pdf .‏
References
Carson, P. B. (2012). Effects of levels of formal educational training in mathematics on teacher self-efficacy (Doctoral dissertation, Piedmont College).‏ Gardner, R. J. (1995). Geometric tomography (Vol. 1). Cambridge: Cambridge University Press http://www.mathcentre.ac.uk/resources/uploaded/mc-ty-triangleformulae-2009-1.pdf httpfiles.books.elebda3.netdownload-pdf-ebooks.org-ku-9199.pdfhttp://www.mathcentre.ac.uk/resources/uploaded/mc-ty-triangleformulae-2009-1.pdf
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