Mestrado em Matemática em Rede Nacional - PROFMAT

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Aplicacao de determinante: area de poligono convexo e volume de piramide
(Universidade Federal de Goiás, 2015-06-17) Araujo, Elismar Jose de; Freitas, Thiago Porto de Almeida; http://lattes.cnpq.br/5154082262879445; Freitas, Thiago Porto de Almeida; Leandro, Bianka Carneiro; Oliveira, Plínio José
This work will concentrate on making a rereading of the theories that surround the procedures for calculating the area of a convex polygon, as well as the volume of a pyramid whose base is a polygon convex, with its vertices properly represented in a coordinate system, in the plan or in space, respectively. Addresses some topics on arrays and determinant and some of its applications, in particular the study of polygon area and the volume of the pyramid. Based on applying a decisive factor for the calculation of the area of a triangle with its vertices represented in a coordinate system, presents a new theorem to calculate the area of any polygon convex, as well as, a new formula to calculate the volume of any pyramid with convex basis as a direct application of the volume of the tetrahedron with its vertices represented in an orthogonal system. For both, it was essential to the concept of coordinates in the plane and in space, vectors in the plane and in space, and some of its properties, being essential for the demonstrate the volume of the tetrahedron and the area of the triangle, using determinant. Keywords: Volume. Area. Convex polygon. Pyramid. Triangle. Tetrahedron