Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.

Result

V =  8470 cm3
S =  2661.889 cm2

Solution:

$u = 22 \ cm \ \\ a = u / \sqrt{ 2 } = 22 / \sqrt{ 2 } = 11 \ \sqrt{ 2 } \ cm \doteq 15.5563 \ cm \ \\ S_{ 1 } = a^2 = 15.5563^2 = 242 \ cm^2 \ \\ h = 35 \ cm \ \\ V = S_{ 1 } \cdot \ h = 242 \cdot \ 35 = 8470 = 8470 \ cm^3$
$S_{ 2 } = 4 \cdot \ a \cdot \ h = 4 \cdot \ 15.5563 \cdot \ 35 = 1540 \ \sqrt{ 2 } \ cm^2 \doteq 2177.8889 \ cm^2 \ \\ S = 2 \cdot \ S_{ 1 } + S_{ 2 } = 2 \cdot \ 242 + 2177.8889 \doteq 2661.8889 = 2661.889 \ cm^2$

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