96893253 tabela-centroides-de-areas
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This document provides formulas for calculating the centroids and areas of various geometric shapes including triangles, circles, semicircles, quarter circles, ellipses, parabolas, arcs, and sectors. The formulas give the x and y coordinates of the centroid and expressions for calculating the area of each shape based on parameters like side lengths, radii, angles, etc. Formulas are provided for basic as well as composite shapes formed by combining geometric elements.
96893253 tabela-centroides-de-areas
- 1. .h b x y . D x y D . R x y Centróides de Áreas Triângulo X 3 h Y = 2 hb A ⋅ = Triângulo Isósceles/Eqüilátero 0=X 3 h Y = 2 hb A ⋅ = Triângulo Retângulo 3 b X = 3 h Y = 2 hb A ⋅ = Círculo 2 D X = 2 D Y = 2 RA π= Semicírculo 0=X π3 4 R Y ⋅ = 2 2 R A π = . h b/2 b/2 b h . y x
- 2. .b x y a . R x y . x y b a .h x y a .h a y x y . Y=kx² h a x Quarto de Círculo π3 4 R X ⋅ = π3 4 R Y ⋅ = 4 2 R A π = Semi-elipse 0=X π3 4 b Y ⋅ = 2 ab A ⋅ = π Quarto de elipse π3 4 a X ⋅ = π3 4 b Y ⋅ = 4 ab A ⋅ = π Parábola 0=X 5 3h Y = 3 4 ah A ⋅ = Semiparábola 8 3a X = 5 3h Y = 3 2 ah A ⋅ = Arco de Parábola do 2º grau 4 3a X = 10 3h Y = 3 ah A =
- 3. . R x y . R x y Arco de Parábola do grau n a n n X ⋅ + + = 2 1 h n n Y ⋅ + + = 24 1 1+ = n ah A Setor Circular α α 3 sen2r X = 0=Y 2 rA ⋅= α Centróides de Linhas Semi-circunferência 0=X π r Y ⋅ = 2 Rc ⋅= π Quarto de Circunferência π R X ⋅ = 2 π r Y ⋅ = 2 2 r c ⋅ = π Arco de circunferência α αsenr X = 0=Y rA ⋅= α2 y α α x r y . Y=kxn h a x y α α x r