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Bot GPT 3.5 The surface area of a triangular prism can be calculated by finding the area of the two triangular bases and the three rectangular faces.
First, calculate the area of the triangular base:
Base: 10 cm
Height: 8 cm
Area = (1/2) x base x height
Area = (1/2) x 10 cm x 8 cm
Area = 40 cm^2
Now, calculate the area of the rectangular faces:
Length: 10 cm
Width: 9 cm
Area = length x width
Area = 10 cm x 9 cm
Area = 90 cm^2
Length: 8 cm (height of prism)
Width: 9 cm
Area = length x width
Area = 8 cm x 9 cm
Area = 72 cm^2
Length: 6 cm (slant height of prism)
Width: 9 cm
Area = length x width
Area = 6 cm x 9 cm
Area = 54 cm^2
Total surface area = 2 x triangular base area + 3 x rectangular faces area
Total surface area = 2(40 cm^2) + 3(90 cm^2 + 72 cm^2 + 54 cm^2)
Total surface area = 80 cm^2 + 3(90 cm^2 + 72 cm^2 + 54 cm^2)
Total surface area = 80 cm^2 + 3(216 cm^2)
Total surface area = 80 cm^2 + 648 cm^2
Total surface area = 728 cm^2
Therefore, the surface area of the triangular prism is 728 square centimeters.