In a rectangular parallelepiped, the sides of the base are 17 dm and 13 dm, and the height of the parallelepiped is 9 dm. Find: a) the area of the lateral surface of the parallelepiped; b) the total surface area of the parallelepiped; c) the area of the diagonal section of the parallelepiped; d) diagonal.
The lateral surface area of a parallelepiped is equal to the product of the base perimeter and the lateral edge.
S side = Ravsd * AA1 = 2 * (AD + CD) * AA1 = 2 * (17 + 13) * 9 = 540 dm2.
Determine the total area of the parallelepiped.
S floor = S side + 2 * Sb = 360 + 2 * (17 * 13) = 540 + 442 = 982 dm2.
Let us draw the diagonal AC of the base and determine its length by the Pythagorean theorem.
AC ^ 2 = AD ^ 2 + CD ^ 2 = 289 + 169 = 458
AC = √458 dm.
Determine the area of the diagonal section ACC1A1.
Ssection = АА1 * АС = 9 * √458 dm2.
Determine the length of the diagonal CA1 from the right-angled triangle AA1C.
CA1 ^ 2 = AC ^ 2 + AA1 ^ 2 = 458 + 81 = 539.
CA1 = 7 * √11 dm.
Answer: Side = 540 dm2, Sok = 982 dm2, Ssection = 9 * √458 dm2, CA1 = 7 * √11 dm.
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