Prism height calculation

Calculate the height of a regular quadrilateral prism whose base is a rhombus. The edge in the base is 7 cm long, the opposite edges are 5 cm apart, and we also know that the entire body has a volume of 1dm³.

Final Answer:

h =  28.5714 cm

Step-by-step explanation:

$$\begin{gathered} a=7\text{cm} \\ v=5\text{cm} \\ V=1{\text{dm}}^3\to {\text{cm}}^3=1\cdot 1000{\text{cm}}^3=1000{\text{cm}}^3 \\ S=a\cdot v=7\cdot 5=35{\text{cm}}^2 \\ V=Sh \\ h=V/S=1000/35=28.5714\text{cm} \end{gathered}$$

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