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Bot GPT 3.5 To find the surface area of the net of the triangular prism, we need to find the areas of each of the faces and add them together.
1. The triangular base has a height of 4 cm and a base of 4 cm. The formula for the area of a triangle is (1/2) * base * height. So, the area of the base triangle is (1/2) * 4 * 4 = 8 cm^2.
2. There are two triangular faces on the prism, each with a base of 4 cm and a height of 4 cm. The formula for the area of a triangle is still (1/2) * base * height. So, the area of each triangular face is (1/2) * 4 * 4 = 8 cm^2. Since there are two triangular faces, the total area for both is 2 * 8 = 16 cm^2.
3. Finally, there are three rectangular faces on the prism. The length of each rectangle is the same as the height of the base triangle, which is 4 cm. The width of each rectangle is the same as the length of the prism, which is also 4 cm. The formula for the area of a rectangle is length * width. So, the area of each rectangular face is 4 * 4 = 16 cm^2. Since there are three rectangular faces, the total area for all three is 3 * 16 = 48 cm^2.
Adding up the areas of the base triangle, two triangular faces, and three rectangular faces gives us:
8 + 16 + 48 = 72 cm^2
Therefore, the surface area of the net of the triangular prism is 72 cm^2.