![]() ![]() 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. For its calculation, two dimensions are involved, thus we measure it in square units. i.e., it is the total surface area minus the areas of the two bases.It is also known as the lateral surface area (LSA). The lateral area for a triangular prism is the sum of areas of its side faces (which are 3 rectangles). 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. The word 'lateral' means 'belonging to the side'. 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. Learn how to calculate the surface area of a triangular prism using a formula that combines the areas of the base triangle and the three rectangular faces. 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.
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