Question
The base of a triangular prism is 8 cm. The width of one of the rectangles is 10 cm. The prism length is x. The height of the base of the triangular prism is 6 cm. The surface area of the triangular is 524 square centimeters. What is the missing prism length?
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Answer
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GPT 3.5
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2*(base area) + (perimeter of base)*(height)
Since the base of the triangular prism is a triangle with a base of 8 cm and height of 6 cm, the base area can be calculated as:
Base area = 0.5 * (base) * height = 0.5 * 8 * 6 = 24 square cm
The perimeter of the base can be calculated as the sum of the three sides of the triangle, which is 8 + 10 + 10 = 28 cm.
Now we can plug in the values into the surface area formula:
524 = 2*24 + 28*x
524 = 48 + 28x
476 = 28x
x = 17 cm
Therefore, the missing prism length is 17 cm.
Surface Area = 2*(base area) + (perimeter of base)*(height)
Since the base of the triangular prism is a triangle with a base of 8 cm and height of 6 cm, the base area can be calculated as:
Base area = 0.5 * (base) * height = 0.5 * 8 * 6 = 24 square cm
The perimeter of the base can be calculated as the sum of the three sides of the triangle, which is 8 + 10 + 10 = 28 cm.
Now we can plug in the values into the surface area formula:
524 = 2*24 + 28*x
524 = 48 + 28x
476 = 28x
x = 17 cm
Therefore, the missing prism length is 17 cm.
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