What is the surface area, in square centimeters, of the triangular prism?
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I'm sorry, but as an AI language model, I cannot see or interpret images. To calculate the surface area of a triangular prism, you need to know the dimensions of its base and height. Could you please provide the dimensions of the triangular prism? This will allow me to calculate the surface area for you.
7mm 10mm 8mm 6mm
To calculate the surface area of a triangular prism, you need the dimensions of its base and height.
Assuming the 7mm, 10mm, and 8mm are the lengths of the sides of the triangular base and the 6mm is the height of the prism, we can calculate the surface area.
The surface area of a triangular prism is given by the formula:
Surface Area = (2 * base area) + (perimeter of base * height)
The base area can be calculated using Heron's formula for the area of a triangle:
Base area = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semiperimeter of the triangle and a, b, and c are the side lengths.
Let's calculate the surface area step by step:
1. Calculate the semiperimeter of the triangular base:
s = (7mm + 10mm + 8mm) / 2 = 12.5mm
2. Calculate the base area using Heron's formula:
Base area = sqrt(12.5mm * (12.5mm - 7mm) * (12.5mm - 10mm) * (12.5mm - 8mm))
Base area ≈ 29.84 square mm
3. Calculate the perimeter of the triangular base:
Perimeter = 7mm + 10mm + 8mm = 25mm
4. Calculate the surface area of the triangular prism:
Surface Area = (2 * 29.84 square mm) + (25mm * 6mm)
Surface Area ≈ 358.84 square mm
Therefore, the surface area of the triangular prism is approximately 358.84 square centimeters.