1. The problem asks for the minimum amount of paper Sarah will need to wrap a package that measures 46 cm. We need to clarify what "46 cm" refers to (likely the perimeter or a dimension), but since the problem is ambiguous, we will assume it refers to the perimeter of the package. 2. To find the minimum amount of paper, we typically want to find the surface area or the minimum wrapping paper area needed. However, with only a perimeter given, the shape that minimizes area for a given perimeter is a square. 3. If the package is a square with perimeter $P = 46$ cm, then each side length $s$ is given by: $$s = \frac{P}{4} = \frac{46}{4} = 11.5 \text{ cm}$$ 4. The area $A$ of the square (minimum paper needed) is: $$A = s^2 = (11.5)^2 = 132.25 \text{ cm}^2$$ 5. Therefore, the minimum amount of paper Sarah will need is $132.25$ square centimeters. Note: The triangle described (with sides 12 cm, 4 cm, and hypotenuse $2\sqrt{10}$ cm) does not directly relate to the package measurement or the minimum paper needed based on the given information, so it is not used in this calculation.