What is the formula for calculating surface area? The formula for calculating the surface area of a triangular prism is bh + (s1 + s2 + s3)l. How do I calculate the surface area of a triangular prism? Use the formula bh + (s1 + s2 + s3)l.What is a triangular prism? A triangular prism is a three-dimensional shape with two identical triangular ends and three rectangular sides.Complex Shapes: This formula is for regular triangular prisms.Accuracy of Measurements: The accuracy of the surface area calculation depends on the accuracy of the measurements.Categories of Surface Area Calculations Range (square feet)Įvolution of Surface Area Calculations Time Period Where b is the area of the base, h is the height of the triangle, s1, s2, and s3 are the sides of the triangle, and l is the length of the prism. The formula to calculate the surface area of a triangular prism is as follows: Surface Area = bh + (s1 + s2 + s3)l Categories of Surface Area Calculations.Thus, the point we have found is a local minimum. The second derivative of this guy is strictly positive for positive s, implying the function is concave up for positive s. To do so you must take the second derivative. We'll end up with h = 2 * 5 2/3 *7 1/3 / sqrt(3).ĮDIT: It's a bit pedantic, but technically you have to make sure that it's a local minimum at the value of s that I've found. From there, we can easily find the height by substituting into our previous formula. We want to find the minimum so we set SA' = 0. SA = 2(sqrt(3)/4)s 2 + 3sh (the first term is the 2 triangular parts and the second term is the three lateral, rectangular parts).Īs a function of s alone, we have SA = 2(sqrt(3)/4)s 2 + 4sqrt(3)350/s. This is equivalent to h = 4*350/(sqrt(3)s 2 ). V = (sqrt(3)/4)hs 2 = 350 cm 3 (I converted mL to cm 3 for ease). Then the area of the base is (sqrt(3)/4)s 2. Let s be the base of the triangle and h be the height. This is an ordinary optimization problem so it requires the use of basic calculus. Re-read your post before hitting submit, does it still make sense.Show your work! Detail what you have tried and what isn't working.Use proper spelling, grammar and punctuation.Give context and details to your question, not just the equation.Help others, help you! How to ask a good question Asking for solutions without any effort on your part, is not okay. Beginner questions and asking for help with homework is okay. Post your question and outline the steps you've taken to solve the problem on your own.
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