Prism - box

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm³. Calculate the surface of the prism.

Correct result:

S =  570 cm²

Solution:

$$\begin{gathered} a=7.5 \\ u=12.5 \\ V=0.9\cdot 10^3=900 \\ b=\sqrt{u^2-a^2}=\sqrt{12.5^2-7.5^2}=10 \\ c=V\mathrm{/}(a\cdot b)=900\mathrm{/}(7.5\cdot 10)=12 \\ S=2\cdot (a\cdot b+b\cdot c+a\cdot c)=2\cdot (7.5\cdot 10+10\cdot 12+7.5\cdot 12)=570{\text{cm}}^2 \end{gathered}$$

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