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=50π/180=50⋅ 3.1416/180≐0.8727 u2=c/tan⁡(A)=28.6/tan⁡(0.8727)≐23.9982 a=u2/2=23.9982/2≐16.9693 S1=a2=16.96932≐287.958 V=S1⋅ c=287.958⋅ 28.6=8235.598 cm3c=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⋅ S1+c⋅ 4⋅ a=2⋅ 287.958+28.6⋅ 4⋅ 16.9693=2517.207 cm2S=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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