To break it down, a prism is a solid object which:
• Features two identical bases.
• Is either in a parallelogram shape or three rectangular faces. These are oblique prisms and right prisms respectively.
• Across its whole length, it has an identical cross section.
Keep in mind that, via the ‘triangular prism’ term, we’re describing a right triangular prism. There are other prism types such as a rectangular prism.
The volume and surface area – these are typically what need calculating when a triangular prism is concerned. The most basic two equations are as followed:
Volume = 0.5 * b * h * length
b is the length of the triangle’s base. h is the triangle’s height. While the length is, you guessed it, the prism’s length.
Area = Length * (a + b + c) + (2 * base_area)
The a, b and c letters are the respective sides of the triangle. The base area of the triangular prism is represented by base_area.
However, what if you don’t possess the base and height of the triangle? Or if you don’t have the triangular base’s sides, yet you need to discover the surface area? Well don’t worry: there are different triangular prism formulas as found below.
Finding the volume of a triangular prism is easy with our calculator. Volume = length * base_area is a general formula for triangular prism volume. The one parameter that’s always necessary is the prism length, while there are four methods for calculating the base – triangle area. Thankfully our calculator has all four techniques implemented.
Let’s take a look at the formulas:
1. First of all, there’s the previously mentioned formula for the triangle’s height and base:
Volume = 0.5 * b * h * length
2. When you know each length of the three sides (SSS), it’s a case of using Heron’s formula to work out the triangular base’s area:
volume = length * 0.25 * √( (a + b + c) * (-a + b + c) * (a - b + c) * (a + b - c) )
3. With two sides and an angle in between (SAS), it’s a case of using trigonometry when calculating the area:
volume = length * 0.5 * a * b * sin(γ)
4. If you have a triangular prism where a side is between two angles (ASA), working out the area again involves trigonometry:
volume = length * a² * sin(β) * sin(γ) / (2 * sin(β + γ))
The most prevalent formula for calculating the surface area is the following:
area = length * (a + b + c) + (2 * base_area) = length * base_perimeter + (2 * base_area)
This is done when you have three sides given. Yet what happens when you don’t have those three sides?
• With two sides and an angle in between (SAS): We can reveal the third side thanks to utilizing law of cosines: area = length * (a + b + √( b² + a² - (2 * b * a * cos(angle)))) + a * b * sin(angle)
• When a side is between two angles (ASA): The two missing sides can be found via law of sines: area = (length * (a + a * (sin(angle1) / sin(angle1+angle2)) + a * (sin(angle2) / sin(angle1+angle2)))) + a * ((a * sin(angle1)) / sin(angle1 + angle2)) * sin(angle2)
Sadly, there is one occurrence where you’re unable to calculate the triangular prism volume. This is when you are given a triangle base and its height. Every other option, however, can be solved with the triangular prism calculator.
Now we’ve went over the formulas, let’s look at an example of using the triangular prism calculator to work out a tent’s volume and surface area.
1. Find the triangular prism’s length. For this example, we’ll say it’s 90 in.
2. Choose the parameters: This is based on how many sides given and their configuration, or if it’s a base and length calculation. For this example, we have given three sides.
3. Input base sides: The tent has a = 50 in, b = 60 in, and c = 60 in.
4. Now the surface area and volume appear immediately: Once these figures are entered, you will see the prism volume is 122,723 cu in, while the prism surface area is 18,027 in².
