Surface area of a triangular prism how to#

This online demonstration of an adjustable triangular prism is a good example to see the relationship between the object's height, lengths, and surface area. The formula for surface area of a triangular prism is actually a combination of the formulas for its triangular bases and rectangular sides. So calculate the triangle part of the surface area now: There are two triangles for its base (Front + Back). Triangular prism Total surface area of the triangular prism Lateral surface area of the prism + Area of two bases ( (a + b + c)h + bh) square units. We'll first divide up the steps to illustrate the concept of finding surface area, and then we'll give you the surface area of a triangular prism formula.įind the surface area of the following triangular prism. Let's try to find the surface area of a triangular prism and take a look the prism below. You can easily see how the surface area requires all the sides' area to be found and how it represents the total area surrounding the 3D figure. A good way to picture how this works is to use a net of a 3D figure.

In order to find the surface area, the area of each of these sides and faces will have to be calculate and then added together. So what is surface area?ģD objects have surface areas, which is the sum of the total area of the object's sides and faces.

Surface area of a triangular prism how to#

How to find the surface area of a triangular prismĪrea helps us find the amount of space contained on a 2D figure. Today we're going to focus on triangular prisms, that is, a prism with a polygonal base that has 3 sides.

For example, we can have pentagonal prisms and square prisms. The naming convention for prisms is to name the prism after the shape of its base. If it's connected by parallelograms, it's called an oblique prism. If it's connected with rectangular surfaces (its sides are made of rectangles), it's called a right prism. They have polygonal bases on either sides which are connected to each other by rectangular or parallelogram surfaces. Prisms are 3D shapes made of surfaces that are polygonal. Thus, the point we have found is a local minimum.To understand what a triangular prism is, let's start with the definition of prisms. 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.