To find out how much fabric will be left over after Jordan makes the tent, we need to calculate the surface area of the triangular prism and compare it to the area of the fabric she purchased.
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Calculate the area of the fabric Jordan purchased: The fabric dimensions are 18 cm by 18 cm: \[ \text{Area of the fabric} = 18 \times 18 = 324 , \text{cm}^2 \]
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Calculate the surface area of the triangular prism: The surface area \( SA \) of a triangular prism can be calculated using the formula: \[ SA = (Base \times Height) + (Perimeter \times Length) \]
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Base area of the triangular face: The base is a triangle with base \( b = 4 , \text{cm} \) and height \( h = 6 , \text{cm} \): \[ \text{Area of triangle} = \frac{1}{2} \times b \times h = \frac{1}{2} \times 4 \times 6 = 12 , \text{cm}^2 \]
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The prism has 2 triangular faces, so: \[ \text{Total area of triangular faces} = 2 \times 12 = 24 , \text{cm}^2 \]
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Calculate the perimeter of the triangular face: The sides of the triangle are 4 cm, 7 cm, and 7 cm (the third side): \[ \text{Perimeter} = 4 + 7 + 7 = 18 , \text{cm} \]
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Now calculate the lateral surface area: \[ \text{Lateral Surface Area} = \text{Perimeter} \times \text{Length} = 18 \times 12 = 216 , \text{cm}^2 \]
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Finally, add the areas: \[ SA = 24 + 216 = 240 , \text{cm}^2 \]
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Calculate the leftover fabric: \[ \text{Leftover fabric} = \text{Area of fabric} - \text{Surface area of prism} = 324 - 240 = 84 , \text{cm}^2 \]
Therefore, the amount of fabric that will be left over is 84 cm².
The correct response is: 84 cm².