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A toy is being constructed in the shape of a pyramid. The maximum amount of material to cover the sides and bottom of the pyramid is 250 square centimeters. The height of the toy is double the side length. What are the maximum dimensions to the nearest square centimeter for a square base and for a hexagonal base?

\begin{tabular}{|c|c|c|}
\hline
Shape of Base & Side Length & Height \\
\hline
square & [tex]$\square$[/tex] cm & [tex]$\square$[/tex] cm \\
\hline
regular hexagon & [tex]$\square$[/tex] cm & [tex]$\square$[/tex] cm \\
\hline
\end{tabular}



Answer :

GinnyAnswer
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}

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