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Bot GPT 3.5 To find the amount of fabric that will be used for the triangular prism tent, we need to calculate the surface area of the prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base) * height
Given that the base of the prism is a right-angled triangle with base and height both equal to 6 cm, we can calculate the base area:
Base Area = 1/2 * base * height = 1/2 * 6 cm * 6 cm = 18 cm²
The perimeter of the base triangle can be found using the Pythagorean theorem:
Perimeter = base + height + hypotenuse = 6 cm + 6 cm + √(6² + 6²) = 6 cm + 6 cm + √72 = 6 cm + 6 cm + 8.49 cm ≈ 20.49 cm
Now, we can calculate the total surface area of the prism:
Surface Area = 2(18 cm²) + 20.49 cm * 6 cm = 36 cm² + 122.94 cm² = 158.94 cm²
The total amount of fabric used for the tent will be 158.94 cm².
Since Jordan purchased a piece of fabric that is 18 cm by 18 cm, the total area of the fabric is:
Total Fabric Area = 18 cm * 18 cm = 324 cm²
To find out how much fabric will be left over, we need to subtract the surface area of the prism from the total fabric area:
Fabric Left Over = Total Fabric Area - Surface Area = 324 cm² - 158.94 cm² = 165.06 cm²
Therefore, Jordan will have 165.06 cm² of fabric left over after making the triangular prism tent for her little sister’s dolls.