Quadrangular prism

The quadrangular prism has a volume 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?

Result

h =  14.4 cm

Solution:

V=648 cm3 a=10 cm c=5 cm v=6 cm S=(a+c)⋅ v/2=(10+5)⋅ 6/2=45 cm2 h=V/S=648/45=725=14.4=14.4  cm V = 648 \ cm^3 \ \\ a = 10 \ cm \ \\ c = 5 \ cm \ \\ v = 6 \ cm \ \\ S = (a+c) \cdot \ v/2 = (10+5) \cdot \ 6/2 = 45 \ cm^2 \ \\ h = V / S = 648 / 45 = \dfrac{ 72 }{ 5 } = 14.4 = 14.4 \ \text{ cm }

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