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Sagot :
To determine the maximum possible dimensions for the toy pyramid with a maximum surface area of 250 square centimeters, let's break it down by base shape.
### Square Base
For the square base pyramid:
- The side length of the square base is approximately 7.071 cm.
- The height of the pyramid is double the side length, which is approximately 14.142 cm.
### Regular Hexagon Base
For the regular hexagon base pyramid:
- The side length of the hexagon base is approximately 5.392 cm.
- The height of the pyramid is double the side length, which is approximately 10.784 cm.
So, to the nearest square centimeter:
\begin{tabular}{|c|c|c|}
\hline
Shape of Base & Side Length & Height \\
\hline
square & 7 cm & 14 cm \\
\hline
regular hexagon & 5 cm & 11 cm \\
\hline
\end{tabular}
### Square Base
For the square base pyramid:
- The side length of the square base is approximately 7.071 cm.
- The height of the pyramid is double the side length, which is approximately 14.142 cm.
### Regular Hexagon Base
For the regular hexagon base pyramid:
- The side length of the hexagon base is approximately 5.392 cm.
- The height of the pyramid is double the side length, which is approximately 10.784 cm.
So, to the nearest square centimeter:
\begin{tabular}{|c|c|c|}
\hline
Shape of Base & Side Length & Height \\
\hline
square & 7 cm & 14 cm \\
\hline
regular hexagon & 5 cm & 11 cm \\
\hline
\end{tabular}
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