Quadrilateral oblique prism

What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°?

Correct answer:

V =  1.0113 m3

Step-by-step explanation:

a=1 m b=1.1 m c=1.2 m d=0.7 m  h=3.9 m φ=20+35/60=1224720.5833  β=50.5   u2 = a2+b2  2 a b cos β u=a2+b22 a b cosβ=a2+b22 a b cos50.5° =12+1.122 1 1.1 cos50.5° =12+1.122 1 1.1 0.636078=0.90035 m  s=(a+b+u)/2=(1+1.1+0.9003)/21.5002 m S1=s (sa) (sb) (su)=1.5002 (1.50021) (1.50021.1) (1.50020.9003)0.4244 m  s2=(c+d+u)/2=(1.2+0.7+0.9003)/21.4002 m S2=s2 (s2c) (s2d) (s2u)=1.4002 (1.40021.2) (1.40020.7) (1.40020.9003)0.3132 m  h2=h sinφ=h sin20.583333333333° =3.9 sin20.583333333333° =3.9 0.351569=1.37112 m  S=S1+S2=0.4244+0.31320.7376 m  V=S h2=0.7376 1.3711=1.0113 m3

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