Jordan purchased a piece of fabric that is 18 cm by 18 cm in order 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.
To calculate the amount of fabric left over, we need to first calculate the total surface area of the triangular prism that will be covered by the fabric.
The surface area of a triangular prism is given by the formula:
2 * (base area of the triangle) + (perimeter of the base) * (height)
The base of the triangle is 18 cm by 18 cm, so the base area is:
Base Area = 18 cm * 18 cm = 324 cm²
The perimeter of the base is:
Perimeter = 18 cm + 18 cm + 18 cm = 54 cm
The height of the triangular prism is not given, so let's assume the height of the tent to be 10 cm.
Now, we can calculate the total surface area covered by the fabric:
Surface Area = 2 * 324 cm² + 54 cm * 10 cm
Surface Area = 648 cm² + 540 cm²
Surface Area = 1188 cm²
The total area covered by the fabric is 1188 cm².
The area of the fabric that Jordan purchased is 18 cm by 18 cm, so the total area of the fabric is:
Total Area of Fabric = 18 cm * 18 cm = 324 cm²
Therefore, the amount of fabric left over is:
Leftover Fabric = Total Area of Fabric - Surface Area
Leftover Fabric = 324 cm² - 1188 cm²
Leftover Fabric = -864 cm²
Since the leftover fabric is a negative value, it means that Jordan will not have enough fabric to cover the entire surface of the triangular prism.