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**Laurent** Split the problem into parts:

- what is the area of an equilateral triangle with side $\displaystyle a$?

- what is the volume of the prism you need, with height $\displaystyle h$ and side $\displaystyle a$?

- what is the lateral area of this prism?

- express the price $\displaystyle P$ in terms of $\displaystyle a$ and $\displaystyle h$.

- given the volume $\displaystyle V$ of the prism, express $\displaystyle h$ in terms of $\displaystyle a$ (and $\displaystyle V$, fixed). Use this to express the price in terms of $\displaystyle a$ (and of $\displaystyle V$, which is fixed).

- study the price function you have obtained (depending on $\displaystyle a\geq 0$): for which $\displaystyle a$ is it minimum?, what is this minimum value? What is the value of $\displaystyle h$ corresponding to that $\displaystyle a$?