Question 129
The monument to Mathenkamen is shaped like a pyramid resting on its square base of side $18~\mathrm{m}$. Its height measures $15~\mathrm{m}$, and the foot of the height falls in the center of the square. The pyramid is oriented so that when the sun's rays come from the south inclined by $45^\circ$ with respect to the ground, the area of the part of soil on which it spreads its shadow is as small as possible. How much is this area expressed in $\mathrm{m}^2$? (Note: the ground covered by the base of the pyramid should not be counted as shady terrain.)