A area one end; a = area of other end; m = area of section midway between ends; 7 = perpendicular distance between ends. V = {(A + a + 4m). The area m is not in general a mean between the areas of the two ends, but its sides are means between the corresponding lengths of the ends. A+ al. α 2 To obtain area of base, divide it into triangles, and find their sum. The formula for V applies to any pyramid whose base is A and altitude h. The formula for V applies to the frustum of any pyramid.. PRISM OR PARALLELOPIPED. S= Ph+2 A. V = A h. For prisms with regular polygon as bases, P = length of one side X number of sides. To obtain area of base, if it is a polygon, divide it into triangles, and find sum of partial areas. FRUSTUM OF PRISM. If a section perpendicular to the edges is a triangle, square, parallelogram, or regular polygon, sum of lengths of edges V number of edges section. X area of right REGULAR POLYGONS. Divide the polygon into equal triangles and find the sum of the partial areas. Otherwise, square the length of one side and multiply by proper number from the following table: Name. No. Sides. Multiplier Divide the area into trapezoids, triangles, parts of circles, etc., and find the sum of the partial areas. If the figure is very irregular, the approximate area may be found as follows: Divide the figure into parts by equidistant parallel lines b, c, d, etc. The lengths of these lines being measured, then, calling a the first and n the last length, and y the width of strips, m). +b+c+ etc. + m |