MENSURATION. In the following formulas, the letters have the meanings here given, unless otherwise stated. D = d R = = larger diameter; smaller diameter; radius corresponding to D; = radius corresponding to d; P = perimeter or circumference; C = area of convex surface area of flat surface which can be rolled into the shape shown; Sarea of entire surface = C+ area of the end or ends; = π = 3.1416, nearly ratio of any circumference to its diam The other letters used will be found on the cuts. The above letters refer to angles. For a right-angled triangle, c being the hypotenuse, a C= length of side opposite an acute angle of an oblique-angled triangle. C = length of side opposite an obtuse angle of an oblique-angled triangle. c = √ a2 + b2 + 2b e. h = Va2 e2. For a triangle inscribed in a semicircle; i. e., any rightangled triangle, TRAPEZOID. Ah(a + b). TRAPEZIUM. Divide into two triangles and a trapezoid. A bh'a (h' + h) + ch; or, A= [bh' + ch+ a(h'+h)]. Or, divide into two triangles by drawing a diagonal. Consider the diagonal as the base of both triangles, call its length 1; call the altitudes of the triangles hi and he; then Al(h1 + h2). = *The perimeter of an ellipse cannot be exactly determined without a very elaborate calculation, and this formula is merely an approximation giving fairly close results. |