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Bot GPT 3.5 1. Find the surface area of a triangular prism with the following dimensions:
- Base of the triangle: 5 cm
- Height of the triangle: 6 cm
- Length of the prism: 8 cm
To find the surface area of a triangular prism, we need to calculate the area of the two triangular bases and the three rectangular faces.
Area of the two triangular bases:
Area = 1/2 * base * height
Area = 1/2 * 5 cm * 6 cm
Area = 15 cm^2
Area of the three rectangular faces:
1st face: 5 cm (base) * 8 cm (length) = 40 cm^2
2nd face: 5 cm (base) * 6 cm (height) = 30 cm^2
3rd face: 6 cm (height) * 8 cm (length) = 48 cm^2
Total surface area = 2(15 cm^2) + 40 cm^2 + 30 cm^2 + 48 cm^2
Total surface area = 30 cm^2 + 40 cm^2 + 30 cm^2 + 48 cm^2
Total surface area = 148 cm^2
Therefore, the surface area of the triangular prism is 148 cm^2.
2. Find the surface area of a triangular prism with the following dimensions:
- Base of the triangle: 7 cm
- Height of the triangle: 4 cm
- Length of the prism: 10 cm
Following the same method as above:
Area of the two triangular bases:
Area = 1/2 * base * height
Area = 1/2 * 7 cm * 4 cm
Area = 14 cm^2
Area of the three rectangular faces:
1st face: 7 cm (base) * 10 cm (length) = 70 cm^2
2nd face: 7 cm (base) * 4 cm (height) = 28 cm^2
3rd face: 4 cm (height) * 10 cm (length) = 40 cm^2
Total surface area = 2(14 cm^2) + 70 cm^2 + 28 cm^2 + 40 cm^2
Total surface area = 28 cm^2 + 70 cm^2 + 28 cm^2 + 40 cm^2
Total surface area = 166 cm^2
Therefore, the surface area of the triangular prism is 166 cm^2.