formula for right triangular prism surface area

Formula for right triangular prism surface area how to#

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. So this flap right over here is 20 centimeters by three centimeters, so thats 60 centimeters squared. And now we just have to figure out the area of the two flaps. We want to find the minimum so we set SA' = 0. So thats gonna be 460 square centimeters, 460 square centimeters. 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. In this article, we wil l learn about the formula to find the surface area of a triangular prism along with solving a few examples to provide a better understanding about the surface area of a triangular prism. Let s be the base of the triangle and h be the height. A polyhedron with three rectangular sides and two triangular bases is called a triangular prism. The surface area is expressed in square units. This is an ordinary optimization problem so it requires the use of basic calculus. The surface area of a triangular prism is equal to the sum of the area of tree lateral surfaces and the two bases. 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.

Formula for right triangular prism surface area how to#

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Particularly with rectangular prisms, it is easy to confuse these two topics if a student does not have a complete understanding of the difference. Volume and surface area are different things – volume tells us the space within the shape whereas surface area is the total area of the faces. Calculating volume instead of surface area.