# Four sided prism

Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.

Correct result:

V =  8235.598 cm3
S =  2517.207 cm2

#### Solution:

$c=28.6 \ \\ A=50 \pi/180=50 \cdot \ 3.1416/180 \doteq 0.8727 \ \\ u_{2}=c / \tan(A)=28.6 / \tan(0.8727) \doteq 23.9982 \ \\ a=u_{2}/\sqrt{ 2 }=23.9982/\sqrt{ 2 } \doteq 16.9693 \ \\ S_{1}=a^2=16.9693^2 \doteq 287.958 \ \\ V=S_{1} \cdot \ c=287.958 \cdot \ 28.6=8235.598 \ \text{cm}^3$
$S=2 \cdot \ S_{1}+c \cdot \ 4 \cdot \ a=2 \cdot \ 287.958+28.6 \cdot \ 4 \cdot \ 16.9693=2517.207 \ \text{cm}^2$

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