# Support colum

Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.

Result

V =  0.49 m3
S =  4.265 m2

#### Solution:

$u_{ 1 } = 102/100 = \dfrac{ 51 }{ 50 } = 1.02 \ \\ u_{ 2 } = 64/100 = \dfrac{ 16 }{ 25 } = 0.64 \ \\ h = 1.5 \ \\ S_{ 1 } = u_{ 1 } \cdot \ u_{ 2 }/2 = 1.02 \cdot \ 0.64/2 = \dfrac{ 204 }{ 625 } = 0.3264 \ \\ V = S_{ 1 } \cdot \ h = 0.3264 \cdot \ 1.5 = \dfrac{ 306 }{ 625 } = 0.4896 = 0.49 \ m^3$
$a = \sqrt{ (u_{ 1 }/2)^2+(u_{ 2 }/2)^2 } = \sqrt{ (1.02/2)^2+(0.64/2)^2 } \doteq 0.6021 \ \\ o = 4 \cdot \ a = 4 \cdot \ 0.6021 \doteq 2.4083 \ \\ S = 2 \cdot \ S_{ 1 } + o \cdot \ h = 2 \cdot \ 0.3264 + 2.4083 \cdot \ 1.5 \doteq 4.2653 = 4.265 \ m^2$

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