Answer :
Let's go through the solution step by step for both shapes: the square base and the hexagonal base.
1. Square Base Pyramid:
- The height of the pyramid is double the side length of the base.
- Given that the total surface area (including the base and four triangular faces) is 250 square centimeters.
- Based on this information, we find:
- Side length = 7 cm
- Height = 14 cm
2. Hexagonal Base Pyramid:
- Again, the height of the pyramid is double the side length of the base.
- The total surface area (including the base and six triangular faces) must add up to 250 square centimeters.
- From this, we determine:
- Side length = 5 cm
- Height = 11 cm
So, the maximum dimensions of the toy to the nearest square centimeter are:
\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}
1. Square Base Pyramid:
- The height of the pyramid is double the side length of the base.
- Given that the total surface area (including the base and four triangular faces) is 250 square centimeters.
- Based on this information, we find:
- Side length = 7 cm
- Height = 14 cm
2. Hexagonal Base Pyramid:
- Again, the height of the pyramid is double the side length of the base.
- The total surface area (including the base and six triangular faces) must add up to 250 square centimeters.
- From this, we determine:
- Side length = 5 cm
- Height = 11 cm
So, the maximum dimensions of the toy to the nearest square centimeter are:
\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}