10. The cost of a house consists of the cost of the above-ground part and the cost of the foundation part. For a house with an area of $N \mathrm{~m}^{2}$, the cost of the above-ground part is proportional to $N \sqrt{N}$, and the cost of the foundation part is proportional to $\sqrt{N}$. It is known that for a house with an area of $3600 \mathrm{~m}^{2}$, the cost of the above-ground part is $72 \%$ of the cost of the foundation part. Therefore, to build several identical houses with a total area of $80000 \mathrm{~m}^{2}$ at the minimum total cost, the area of each house in square meters should be $\qquad$
10. Let the area of each house in square meters be $y$, and a total of $x$ identical houses are built, with the total cost being $S$. Then
$$
\left\{\begin{array}{l}
x y=80000, \\
S=(\alpha y \sqrt{y}+\beta \sqrt{y}) \cdot x, \\
\frac{\alpha \cdot 3600 \sqrt{3600}}{\beta \sqrt{3600}}=\frac{72}{100},
\end{array}\right.
$$

where $\alpha, \beta$ are proportionality constants. Therefore, we have
$$
\begin{array}{l}
S=\alpha \cdot 80000 \sqrt{\frac{80000}{x}}+5000 \alpha \sqrt{\frac{80000}{x}} \cdot x \\
=5000 \sqrt{80000} \alpha\left(\frac{16}{\sqrt{x}}+\sqrt{x}\right) \\
\geqslant 10^{6} \times \sqrt{2} \alpha \times 2 \sqrt{\frac{16}{\sqrt{x}}} \cdot \sqrt{x} \\
=10^{6} \times 8 \sqrt{2} \alpha .
\end{array}
$$

Since the equality holds in the above expression, we have $\frac{16}{\sqrt{x}}=\sqrt{x}$.
Thus, $x=16, y=5000$.