Plane and solid geometry . Given prism AK with MQ a rt. section, E a lateral edge, S thelateral area, and P the perimeter of rt. section prove S = P » E. Argument 1. Et. section MQ A. Al, CJ, etc. 2. .\3m±AI, NQ±CJ; etc. 3. .. MN is the altitude of HJ AJ] NQ is the altitude of O CK-, etc. 4. .-. area oi O AJ = MN • AI = MN • E; area oi CJ CK = NQ - CJ= NQ- E] etc. 5. 0AJ+0CK-\ ={MN+NQ^ )E. 6. .. S = P E, Reasons 1. §728. 2. §619. 3. §228. 4. §481. 5. §54,2. 6. §309. 763. Cor. The lateral area of a right prism is equal tothe product of the perimeter of its base and its altitude. Hint. Thu
Plane and solid geometry . Given prism AK with MQ a rt. section, E a lateral edge, S thelateral area, and P the perimeter of rt. section prove S = P » E. Argument 1. Et. section MQ A. Al, CJ, etc. 2. .\3m±AI, NQ±CJ; etc. 3. .. MN is the altitude of HJ AJ] NQ is the altitude of O CK-, etc. 4. .-. area oi O AJ = MN • AI = MN • E; area oi CJ CK = NQ - CJ= NQ- E] etc. 5. 0AJ+0CK-\ ={MN+NQ^ )E. 6. .. S = P E, Reasons 1. §728. 2. §619. 3. §228. 4. §481. 5. §54,2. 6. §309. 763. Cor. The lateral area of a right prism is equal tothe product of the perimeter of its base and its altitude. Hint. Thus, if P = perimeter of base and H = altitude, S = P > H, 764. Def. The slant height of a regular pyramid is the alti-tude of any one of its triangular faces. 765. Def. The slant height of a frustum of a regular pyra-mid is the altitude of any one of its trapezoidal faces. 356 SOLID GEOMETRY Proposition IV. Theorem 766. The lateral area of a regular piframid is equal toone half the product of the perimeter o
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
