Surface Area of a Triangular Prism Calculator

Created by Łucja Zaborowska, MD, PhD candidate
Reviewed by Steven Wooding
Last updated: Nov 12, 2022

Our surface area of a triangular prism calculator offers you 4 different ways to calculate all the queries connected to the surface area of a prism! Go ahead and give it a try; our sample pictures and detailed instructions make it all easier than it's ever been! 🔺

Follow our short article to:

  • Discover different prism triangular faces;
  • Learn about the lateral surface area of a triangular prism; ...and finally
  • Uncover how to find the area of a triangular prism.

Are you ready? Let's go!

🙋 Fond of triangular prisms? We've got more tools related to them: the all-in-one triangular prism calculator and the dedicated volume of a triangular prism calculator.

How to use the surface area of a triangular prism calculator?

This section is a step-by-step instruction on how to find the surface area of a triangular prism using our handy tool; take a look at the mathematical problem you want to solve and gather the following information:

1. Determine the type of a triangular face

💡 Triangular face is the base of our prism. Every single prism has two triangular faces (both are the shape of a triangle).

Find all the information regarding the triangular face that is present in your query:

  1. If only two sides of a triangle are given, it usually means that your triangular face is a right triangle (a triangle that has a right angle = 90° between two of its sides).

    • You need to pick the ◣ right triangle option (this option serves as the surface area of a right triangular prism calculator)
    • You can input any two given sides of the triangle – be careful and check which ones of them touch the right angle (a, b) and which one doesn't (c).
  2. If they gave you all three sides of a triangle – you're the lucky one!

    • Choose the ▲ 3 sides option; then
    • Input all three sides wherever you want (a, b, c).
  3. If they give you two sides and an angle between them

    • Pick the ▲ 2 sides + angle between
  4. If you're given 2 angles and only one side between them

    • Choose the ▲ 2 angles + side between option

2. Enter all the data given in your query

We're giving you over 15 units to choose from! Remember to always choose the unit given in the query and don't be afraid to mix them; our calculator allows that as well!

💡 Length is the height of the whole triangular prism – it's often the longest given value.

3. Your results are here 🎉

In this step, you may also choose from the wide range of area units – choose the one that best fits your needs.

How to calculate the surface area of a triangular prism?

Once again, we need to ask you about the data given in your query – choose the correct version of calculations based on a triangular base of your prism.

◣ right triangle

You've probably been given only two sides of the triangular base; unfortunately, the right-angled triangular prism surface area requires us to know the triangular face (base) area:

Base area = (a × b) / 2

You need to remember that:

  • a, b are sides that touch the right angle (also called legs or catheti)
  • c is the side that doesn't touch the right angle (the hypotenuse).

💡 The third side of a right triangle can be computed using the Pythagorean theorem: a² + b² = c².
If you need help, go to the Pythagorean theorem calculator.

After we've computed the base area, we may proceed to the actual surface calculation.

Here's the most basic formula for triangular prism surface that we can use:

Area = Length × (a + b + c) + (2 × Base area)

or

Area = Length × Base perimeter + (2 × Base area)

💡 Base perimeter is the sum of all sides of a prism's base (a+b+c).

▲ 3 sides

As in the previous example, we first need to know the base area.

This can be calculated using the Heron's formula:

Base area = 0.25 × √[(a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c)],

where a, b, c are the sides of a triangular base

We used the same equations as in the previous example:

Area = Length × (a + b + c) + (2 × Base area)

or

Area = Length × Base perimeter + (2 × Base area)

▲ 2 sides + angle between

Now it's the time when things get complicated.

You can calculate the area of such a triangle using the trigonometry formula:

Base area = 0.5 × a × b × sin(Angle γ)

In this particular case, our triangular prism area calculator uses the following formula combined with the law of cosines:

Area = Length × (a + b + √( b² + a² - (2 × b × a × cos(Angle γ)))) + a × b × sin(Angle γ)

▲ 2 angles + side between

We're diving even deeper into math's secrets! 😱

Here's the formula for the triangle area that we need to use:

Area = = a² × sin(Angle β) × sin(Angle γ) / (2 × sin(Angle β + Angle γ))

In this particular case, we're using the law of sines.

And here's the surface area of a triangular prism formula that we need:

Area = (Length × (a + a × (sin(Angle γ) / sin(Angle γ + Angle β)) + a × (sin(Angle β) / sin(Angle γ+Angle β)))) + a × ((a × sin(Angle γ)) / sin(Angle γ + Angle β)) × sin(Angle β)

❗ Make sure to use the angle conversion calculator if your angles are given in a different unit than degrees.

How do I calculate the lateral surface of a triangular prism?

This calculation's extremely easy! You may either:

  • If you know all the sides of the triangular base, multiply their values by the length of the prism:

    Lateral surface of a triangular prism = Length × (a + b + c)

  • If you know the total surface area, subtract the triangular faces' surface from the prism's total surface area:

    Lateral surface = Total surface of a triangular prism - (2 × Surface of a triangular base)

FAQ

How do I calculate the lateral surface of a triangular prism given length and perimeter?

If you know the length of a prism and its base perimeter, you can determine its lateral surface area by multiplying the perimeter by length.

What is the lateral surface area of a triangular prism with length 10 cm and base perimeter 10 cm?

The answer is 100 cm². You can derive this answer in the following way:

  1. Find the base perimeter (10 cm in this example).
  2. Measure the prism's length (10 cm).
  3. Multiple the prism's base perimeter by its length.
  4. 10 cm multiplied by 10 cm equals 100 cm².

We can also write these steps as the following math formula:

lateral area = base perimeter × prism length

What is the formula for the total surface area of a triangular prism?

The total surface area of a triangular prism is the sum of the areas of all its faces: the three lateral faces (rectangles) and two bases (triangles). The most general formula for the surface area of any prism is:

Total area = Lateral area + 2 × Base area

It depends on the data you're given as to how to proceed to determine both the lateral area and the base area.

Łucja Zaborowska, MD, PhD candidate
Triangle type
◣ right triangle
Triangular prism whose base is a right triangle





a
in
b
in
c
in
Prism length (L)
in
Prism surface area
in²
Base area
in²
Lateral surface
in²
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