To calculate the surface area of a triangular prism, you need to calculate the area of the three rectangular faces and the area of the two triangular bases.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(base area) + (perimeter of base)*(height)
First, calculate the area of the triangular base using Heron's formula:
s = (side1 + side2 + side3) / 2
Area_base = sqrt(s*(s-side1)*(s-side2)*(s-side3))
Area_base = sqrt( (10+12+17)/2 * ( (10+12+17)/2 - 10) * ( (10+12+17)/2 - 12) * ( (10+12+17)/2 - 17 ) ) = 46.404
Next, calculate the perimeter of the base:
Perimeter_base = side1 + side2 + side3 = 10+12+17 = 39
Now, calculate the surface area of the three rectangular faces:
Face 1 area = base_area * height = 46.404 * 9 = 418.636
Face 2 area = base_area * height = 46.404 * 9 = 418.636
Lastly, calculate the surface area of the two triangular bases:
Base area = 2 * base_area = 2 * 46.404 = 92.808
So the total surface area of the triangular prism is:
Surface Area = 2 * 92.808 + 39 * 10 + 418.636 + 418.636 = 185.616 + 390 + 837.272 = 1412.888 square inches
Therefore, the total surface area of the triangular prism is 1412.888 square inches.
Surface area for triangular prism with the following dimensions h=9 inches side 1=10 inches side 2=12 inches side 3=17 inches and l=10 inches
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