Area Of Trapezoid Research Articles

GeoGebra-supported Learning Kit for Teaching Area of Trapezoid Based on TPMK Framework

GeoGebra-supported Learning Kit for Teaching Area of Trapezoid Based on TPMK Framework

Designing a kinematic module with rounding to model the processes of combined radial-longitudinal extrusion involving a tool whose configuration is complex

It is advisable that parts whose shape is complex and which are made from solid or hollow blanks should be made by means of transverse and combined radial-longitudinal extrusion. The variation of manufacturing modes, tool configurations (in the form of chambers and rounding of the transitional sections of matrices) requires an adequate preliminary assessment of the force regime and the features of part shape formation. This paper has proposed a curvilinear kinematic module of the trapezoidal form for modeling radial-longitudinal extrusion processes in the presence of matrix rounding. Given the impossibility of using a quarter-circle boundary for the kinematically assigned possible velocity field, it has been proposed to use approximate curves in the form of z1(r) and z2(r). Taking into account the slightest deviation in the length of the arc of the approximate curve z1(r) and the area of the curvilinear trapezoid bounded by it relative to a quarter of the circle (not exceeding 0.8 % for any ratio), it has been recommended using this particular replacement. We have performed calculations of the value of the reduced deformation pressure inside the kinematic module with rounding taking into consideration the power of cutting forces at the border with adjacent kinematic modules. As an example, the devised module with rounding embedded in the estimation scheme of radial extrusion was analyzed. A significant impact of friction conditions on the force mode and the corresponding optimal value of the rounding radius have been identified. The resulting kinematic module makes it possible to expand the capabilities of the energy method for modeling cold extrusion processes involving the tools of complex form according to new deformation schemes. That could contribute to preparing recommendations on the optimal tool configuration and more active industrial implementation of these processes

Elucidation of Genotypic Variability, Character Association, and Genetic Diversity for Stem Anatomy of Twelve Tossa Jute (Corchorus olitorius L.) Genotypes.

Background and Aims Anatomy of twelve tossa jute genotypes were performed for the variability, heritability, and genetic advance based on yield attributing six anatomical traits. Materials and Methods The experiments were carried out in field and laboratory including 12 tossa jute genotypes followed by RCB design in JAES, Manikganj, and Bangladesh Jute Research Institute, Dhaka, Bangladesh, during 2019-2020. Hypothesis. The tested genotypes were expected to perform better than controls in respect of anatomical characters contributing to fiber yield in tossa jute plants. Results Five genotypes, i.e., Acc. 1318, Acc. 1306, JRO S1, O-412-9-4, and O-0512-6-2 providing good results for the total fiber bundle area, trapezoid number, bark diameter, area of trapezoid, and bark thickness per transverse section in the anatomy of jute plants depicting the more variability (P > 0.01) as well as the possibility of tossa jute varietal development. These morphological and anatomical traits showing highly significant association (∗∗) with one another and coupled with high genetic and phenotypic variance components; high heritability; high and moderate genetic advance and higher divergence in clustering (D2), and PCA would be used as criteria for selection and improvement for fiber yield of tossa jute. Conclusions The high variation and divergence for anatomical characters may be considered an effective selection method of genotypes for higher fiber yield comparing with controls. The genotypes, i.e., Acc. 1318, Acc. 1306, JRO (segregate), O-412-9-4, and O-0512-6-2 with good anatomical traits related to fiber yield could be used as parents in breeding program as well as direct variety development.

Mathematical Communication Characteristics of Pre-Service Primary School Teacher in Explaining the Area of Trapezoid Reviewed from School Origin

Abstract. This study aims to know the characteristics of mathematical communication of pre-service primary school teachers. The material used as the object of research is geometry. It requires the ability of algebra and spatial skills. The area of trapezoid is selected as the topic since it is perceived as the most complex of all plane shapes studied in primary school. It is because the calculation of the area of trapezoid entails three variables. The ability of mathematical communication involves the ability to write and explain. This ability is examined based on the background of students’ secondary school. The subjects of this study were 15 students of Primary Teacher Education, STKIP Al Hikmah Surabaya in academic year 2017-2018. The types of mathematical communication are grouped according to their characteristics. Written communication is sharpened by oral communication. The results were analyzed to investigate the relevance of such abilities with the subjects’ background of their secondary school (SMA, SMK, or MA). The results indicate that the characteristics of written communication consist of: (1) narrative, (2) procedure, and (3) dialogue. Meanwhile, the characteristics of oral communication consist of: (1) lecture, (2) instructional, and (3) discussion. Pre-service teachers graduated from SMA have better mathematical communication skills than those from SMK and MA. Keywords: Pre-service primary school teacher, mathematical communication, the area of trapezoid.

One Usage of Geogebra in Enhancing Pre-service Mathematics Teachers’ Content Knowledge

A wide range of mathematical ideas could be used to develop and justify a formula for calculating the area of trapezoid. Those ideas lead to different strategies for finding out area of trapezoid that we classify in three groups: decomposing, enclosing and transforming strategies. Those strategies should be part of mathematics content knowledge for teaching. In this study we trace a change in structure of mathematics content knowledge of nine pre-service mathematics teachers as a result of using GeoGebra applets that visualize different approaches in finding out the area of trapezoid. We argue that engaging pre-service mathematics teachers to develop and justify formula for calculating the area of trapezoid using GeoGebra applets is a worth task that enhances pre-service mathematics teachers’ content knowledge for teaching. Our experiment confirmed that the use of Geogebra encourage pre-service mathematics teachers to uncover new ideas that lead them towards clearer justifications and easier way of proving formula for area of trapezoid. Keywords: Area of trapezoid, GeoGebra, content knowledge for teaching

Sharing Teaching Ideas: Seven Ways to Find The Area of a Trapezoid

We all want to get away from rote teaching, from students' memorizing and repeating to the teacher what the teacher has told the class. This struggle is particularly apparent in mathematics, in which much teaching is directed toward the mastery of formal tools of thought.

Proof without words: The Gaussian Quadrature as the Area of Either Trapezoid

(1987). Proof without words: The Gaussian Quadrature as the Area of Either Trapezoid. Mathematics Magazine: Vol. 60, No. 2, pp. 89-89.