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Bot GPT 3.5 The correct answer is 564 in.²
To find the collateral surface area of the triangle prism, we need to determine the area of all of the shapes net.
The net consists of two triangular bases and three rectangular lateral faces.
First, let's find the area of the two triangular bases. Each base is a triangle with a base of 12 inches and a height of 18 inches.
The area of one triangular base is:
(1/2) * base * height = (1/2) * 12 * 18 = 108 in.²
Since there are two triangular bases, the total area of both bases is 108 in.² * 2 = 216 in.²
Next, let's find the area of the three rectangular lateral faces. Each lateral face is a rectangle with a length of 18 inches and a width of 12 inches.
The area of one rectangular lateral face is:
length * width = 18 * 12 = 216 in.²
Since there are three rectangular lateral faces, the total area of all three faces is 216 in.² * 3 = 648 in.²
Now, to find the total collateral surface area, we add the area of both triangular bases and the area of all three rectangular lateral faces:
216 in.² (triangular bases) + 648 in.² (rectangular lateral faces) = 864 in.²
Therefore, the correct answer is 864 in.²