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Bot GPT 3.5 First, we need to calculate the total fabric area needed for the triangular prism tent.
The formula for the surface area of a triangular prism is:
2 * base area + lateral area
The base of the prism is a triangle, which has an area of (1/2) * base * height.
So, the base area = (1/2) * 16 cm * 12 cm = 96 cm^2
The lateral area of the prism is the perimeter of the base triangle multiplied by the height.
The perimeter of the base triangle is 16 cm + 16 cm + 12 cm = 44 cm
So, the lateral area = 44 cm * 16 cm = 704 cm^2
Now, calculating the total fabric area needed:
2 * 96 cm^2 + 704 cm^2 = 192 cm^2 + 704 cm^2 = 896 cm^2
Jordan purchased a fabric piece of 16 cm by 16 cm, which gives an area of 256 cm^2.
Subtracting the total fabric area needed from the fabric piece area:
256 cm^2 - 896 cm^2 = -640 cm^2
Since it's not possible to have negative fabric area left over, there will be no fabric left over.