Jordan Purchased A Piece Of Fabric That Is 18 Cm By 18 Cm To Make A Tent For Her Little Sister's Dolls. Using The Dimensions For The Tent Shaped As A Triangular Prism, How Much Fabric Will Be Left Over?A. 324 Cm 2 324 \, \text{cm}^2 324 Cm 2 B. $240 ,

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Introduction

Jordan purchased a piece of fabric that is 18 cm by 18 cm to make a tent for her little sister's dolls. The tent is shaped as a triangular prism, and we need to calculate how much fabric will be left over after making the tent. In this article, we will explore the dimensions of the triangular prism, calculate the surface area of the fabric, and determine the amount of fabric left over.

Understanding the Triangular Prism

A triangular prism is a three-dimensional shape with two identical triangular bases and three rectangular sides. The dimensions of the triangular prism are:

  • Base length: 18 cm
  • Base width: 18 cm
  • Height: 18 cm (assuming the height is equal to the base length and width)

Calculating the Surface Area of the Fabric

To calculate the surface area of the fabric, we need to find the area of the two triangular bases and the three rectangular sides.

Triangular Bases

The area of a triangle is given by the formula:

A = (1/2) * base * height

In this case, the base and height of the triangle are both 18 cm. Therefore, the area of one triangular base is:

A = (1/2) * 18 * 18 = 162 cm^2

Since there are two triangular bases, the total area of the bases is:

2 * 162 = 324 cm^2

Rectangular Sides

The area of a rectangle is given by the formula:

A = length * width

In this case, the length and width of the rectangle are both 18 cm. Therefore, the area of one rectangular side is:

A = 18 * 18 = 324 cm^2

Since there are three rectangular sides, the total area of the sides is:

3 * 324 = 972 cm^2

Total Surface Area

The total surface area of the fabric is the sum of the areas of the two triangular bases and the three rectangular sides:

Total surface area = 324 + 972 = 1296 cm^2

Calculating the Fabric Left Over

To calculate the fabric left over, we need to subtract the total surface area of the fabric from the total area of the fabric.

Fabric left over = Total area - Total surface area

The total area of the fabric is 18 cm by 18 cm, which is:

Total area = 18 * 18 = 324 cm^2

Therefore, the fabric left over is:

Fabric left over = 324 - 1296 = -972 cm^2

However, this is not possible since we cannot have a negative amount of fabric left over. The correct calculation is:

Fabric left over = Total area - Total surface area

Since the total surface area is greater than the total area, we need to subtract the total surface area from the total area of the fabric. However, this will result in a negative value, which is not possible.

Conclusion

In this article, we calculated the surface area of the fabric for a triangular prism tent and determined the amount of fabric left over. However, the calculation resulted in a negative value, which is not possible. This is because the total surface area of the fabric is greater than the total area of the fabric.

Discussion

The discussion category for this article is mathematics. The article involves mathematical calculations, including the area of triangles and rectangles, and the total surface area of the fabric.

Answer

The correct answer is not among the options provided. The calculation resulted in a negative value, which is not possible. However, if we assume that the total surface area is less than the total area of the fabric, the fabric left over would be:

Fabric left over = Total area - Total surface area

Since the total surface area is less than the total area, the fabric left over would be a positive value.

Final Answer

The final answer is not among the options provided. However, if we assume that the total surface area is less than the total area of the fabric, the fabric left over would be a positive value.

References

Introduction

In our previous article, we calculated the surface area of the fabric for a triangular prism tent and determined the amount of fabric left over. However, the calculation resulted in a negative value, which is not possible. In this article, we will answer some frequently asked questions related to the calculation of fabric left over for a triangular prism tent.

Q: What is the total surface area of the fabric for a triangular prism tent?

A: The total surface area of the fabric for a triangular prism tent is the sum of the areas of the two triangular bases and the three rectangular sides. The area of one triangular base is 162 cm^2, and the area of one rectangular side is 324 cm^2. Therefore, the total surface area is:

Total surface area = 2 * 162 + 3 * 324 = 1296 cm^2

Q: What is the total area of the fabric for a triangular prism tent?

A: The total area of the fabric for a triangular prism tent is the area of the fabric, which is 18 cm by 18 cm. Therefore, the total area is:

Total area = 18 * 18 = 324 cm^2

Q: How much fabric will be left over after making the tent?

A: To calculate the fabric left over, we need to subtract the total surface area from the total area of the fabric. However, since the total surface area is greater than the total area, we need to subtract the total area from the total surface area. This will result in a negative value, which is not possible.

Q: Why is the calculation resulting in a negative value?

A: The calculation is resulting in a negative value because the total surface area of the fabric is greater than the total area of the fabric. This is because the triangular prism tent has a larger surface area than the total area of the fabric.

Q: What is the correct way to calculate the fabric left over?

A: The correct way to calculate the fabric left over is to subtract the total surface area from the total area of the fabric. However, since the total surface area is greater than the total area, we need to subtract the total area from the total surface area. This will result in a negative value, which is not possible.

Q: Can we assume that the total surface area is less than the total area of the fabric?

A: Yes, we can assume that the total surface area is less than the total area of the fabric. This will result in a positive value for the fabric left over.

Q: How much fabric will be left over if we assume that the total surface area is less than the total area of the fabric?

A: To calculate the fabric left over, we need to subtract the total surface area from the total area of the fabric. Assuming that the total surface area is less than the total area, the fabric left over would be:

Fabric left over = Total area - Total surface area

Since the total surface area is less than the total area, the fabric left over would be a positive value.

Conclusion

In this article, we answered some frequently asked questions related to the calculation of fabric left over for a triangular prism tent. We discussed the total surface area and total area of the fabric, and how to calculate the fabric left over. We also assumed that the total surface area is less than the total area of the fabric and calculated the fabric left over.

References