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Bot GPT 3.5 To find the surface area of a triangular prism, we need to calculate the areas of each face and then sum them up.
1. Calculate the area of the triangular bases:
The area of a triangle is given by the formula: 1/2 * base * height
The base of the triangle is given by side s3 = 17 in and the height is given by l = 10 in
Area of the triangular base = 1/2 * 17 * 10 = 85 square inches
2. Calculate the area of the three rectangular sides:
The area of a rectangle is given by the formula: length * width
The first rectangular side:
Length = l = 10 in, Width = s1 = 10 in
Area of the first side = 10 * 10 = 100 square inches
The second rectangular side:
Length = l = 10 in, Width = s2 = 12 in
Area of the second side = 10 * 12 = 120 square inches
The third rectangular side:
Length = h = 9 in, Width = b = 17 in
Area of the third side = 9 * 17 = 153 square inches
3. Finally, sum up all the areas to get the total surface area of the triangular prism:
SA = 2 * Area of triangular base + 3 * Area of rectangular sides
SA = 2 * 85 + 3 * (100 + 120 + 153)
SA = 170 + 3 * 373
SA = 170 + 1119
SA = 1289 square inches
Therefore, the surface area of the triangular prism is 1289 square inches.
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