Plane and solid geometry . C D Given regular pyramid 0-ACD ••• witli the perimeter of itsbase denoted by P, its slant height by L, and its lateral area by prove S = ^ P - L, Argument 1. KiediOi/\AOC=\AC OR = ^AC L] area of A COD = ^ CD - L; etc. 2. .\ AA0C+AC0D-\- • 3. .. S=lP L. Reasons 1. § 485. 2. § 54, 2. 3. § 309. 767. Cor. The lateral area ofa frustum of a regular pyramidis equal to one half the productof tlie sum of tlie perimeters ofits bases and its slant height. Hint. Prove *S= \{F-Vp)L. Ex. 1286. Find the lateral area andthe total area of a regular pyramid eachside of wh
Plane and solid geometry . C D Given regular pyramid 0-ACD ••• witli the perimeter of itsbase denoted by P, its slant height by L, and its lateral area by prove S = ^ P - L, Argument 1. KiediOi/\AOC=\AC OR = ^AC L] area of A COD = ^ CD - L; etc. 2. .\ AA0C+AC0D-\- • 3. .. S=lP L. Reasons 1. § 485. 2. § 54, 2. 3. § 309. 767. Cor. The lateral area ofa frustum of a regular pyramidis equal to one half the productof tlie sum of tlie perimeters ofits bases and its slant height. Hint. Prove *S= \{F-Vp)L. Ex. 1286. Find the lateral area andthe total area of a regular pyramid eachside of whose square base is 24 inches, andwhose altitude is 16 inches. Ex. 1287. The sides of the bases of a frustum of a regular octagonalpyramid are 15 centimeters and 24 centimeters, respectively, and theshmt height is 30 centimeters. Find the number of square decimeters inthe lateral area of the BOOK VII 357 Ex. 1288. Find the lateral area of a prism whose right section is aquadrilateral with sides 5, 7, 9, and 13 inches, and whose lateral edge is15 inches. Ex. 1289. Find the lateral area of a right prism whose altitude is 16inches and whose base is a triangle with sides 8, 11, and 13 inches. Ex. 1290. The perimeter of a right section of a prism is 45 deci-meters ; its altitude is 10 V3 decimeters ; and a lateral edge makes withthe base an angle of 60°. Find the lateral area. Ex. 1291. Find the altitude of a regular prism, one side of whosetriangular base is 5 niches and whose lateral area is 195 square inches. Ex. 1292. Find the total area of a regular hexagonal prism whosealtitude is 20 inches and one side of whose base is 10 inches. Ex. 1293. Find the total area of a cube whose diagonal is SVS. Ex. 1294. Find the edge of a cube if its total area is 294 squarecentimeters ; if its total area is T. Ex. 1295. Find the total area of a regxilar tetrahedron whose edgeis 6 inches
Size: 1550px × 1612px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
