How to Find the Surface Area of a Triangular Prism?

Conceptual still life with paper pyramids.

The summation of the total area of all its faces is equal to that cube’s surface. The surface area formula is six times the square of the cube side length. To know how to find the surface area, keep reading below.

It is shown in 6a2, where a represents the length of a side. In other words, it is the entire area. Know also about the volume of a cube.

The area of a cube is the section that its walls cover inside the three-dimensional space if it occupies this place.

How to Find the Surface Area

In the real world, there are numerous solid objects surrounding us with their area and also volume.

The area that an item takes is known as its space while the internal volume of a given object is described in terms of volumes.

What is Surface Area?

The surface area of a shape is equal to the summation of all its face areas. This includes pyramids and prisms. Square units are always used to record surface area.

Prisms are 3D shapes that have a polygonal base and rectangular faces.

Four rectangular lateral faces and two rectangular bases make up the six rectangular faces of a rectangular prism.

How to Find the Surface Area of a Triangular Prism

How to Find the Surface Area

Let’s examine this derivation to see where the formula for a triangular prism’s surface area originates:

In this instance, calculating the lateral surface area portion is simple. The image illustrates how it is made up of three rectangles that are all the same length on one side:

A(lateral) = a × h + b × h + c × h = h × (a + b + c)

which, in brief, we can also write as:

A(lateral) = h × P, where P is a perimeter of a base triangle

Next, determine a triangle base’s area. Depending on what you have, there are numerous ways you can accomplish it. We have incorporated Heron’s formula, which is utilized when three triangle sides are provided, into our calculator (SSS).

A(base) = 0.25 × √((a + b + c) × (-a + b + c) × (a – b + c) × (a + b – c)))

The following is the final formula for a triangular prism’s surface area:

A = A(lateral) + 2 × A(base)

A = h × (a + b + c) + 0.5 × √((a + b + c) × (-a + b + c) × (a – b + c) × (a + b – c))

What is the Lateral Surface Area of a Triangular Prism?

When we talk about the lateral surface area of a solid, we mean the area without the bases.

So, for a triangular prism, we’re figuring out the area without considering the base

Imagine the prism standing with its bases up and down – the lateral area is the space on the vertical faces.

How to Calculate Lateral Surface Area?

How to Find the Surface Area

The trick to finding the lateral surface area of a triangular prism is to multiply the perimeter of the base by the length of the prism. Let’s break it down:

1. The perimeter of the Base: The perimeter of the base is just the total length of all the edges of the base triangle.

2. Length of the Prism: The length of the prism is essentially its height.

Now, plug these values into the formula:

Lateral Surface Area=(S1+S2+S3)×l 

or simply,

LSA=Perimeter×Length = p × l

So, in a nutshell, the Lateral Surface Area (LSA) is given by the formula p×l, where l is the height (length) of the prism, and p is the perimeter of the base. Easy peasy.

Practical Example of Surface Area of Triangular Prism

Let’s put all these theories into practice with an example:

1. Find the surface area of a right triangular prism that has a base area of 60 square units, a length of 7 units, and a base perimeter of 40 units.

Given Values

  • Base Area = 60 square units
  • Base Perimeter = 40 units
  • Length of Prism = 7 units

Solution Steps

1. Surface Area Formula applies.

The formula for the surface area of a right triangular prism is: Surface area=(Perimeter of Base× Prism length+2×Base area)Surface area=(Perimeter of Base× Prism length+2×Base area)

2. Substitute the Given Constant.

Surface Area=(40×7)+(2×60)Surface Area=(40×7)+(2×60)

3. Calculate the Values

Surface Area=(280+120)Surface Area=(280+120)

4. Final Calculation

An area of 400 square units. An area of 400 square units.

How to Figure out the Surface Area of a Right Triangular Prism?

How to Find the Surface Area

Great, now let’s debunk the procedures of calculating the surface area of the right triangular prism – that sweet 3D shape that has two oriental triangles and three rectangles.

To get a comprehensive picture of it, just imagine two fancy triangles being casually laid on top and bottom while three rectangles greet your sides by hugging them at right angles.

Now, we shall compute its surface area, and that will be done in sequential steps.

1. Base Triangles Area

The first step is to calculate the area of these two triangles. Now, check the base length by height. Make a diagonal cut by half. And it is as simple as finding the area of a regular triangle – you know it is right – don’t you?

Area of Base Triangles=2×(12×Base×Height) 

And if we simplify that, it’s just Base×HeightBase×Height.

2. Let’s Talk about the Lateral Surface Area

Let’s move on to the lateral surface area of the sides. Multiply the prism’s length by the base triangle’s perimeter.

Lateral Surface Area=(S1+S2+h)×l 

3. Total Surface Area 

Add up all the areas from Step 1 and Step 2. That’s your total surface area. Imagine you’re putting stickers on each part – the triangles and the rectangles – and you’re done.

Total Surface Area=Lateral Surface Area+Area of Base Triangles

In other words, it’s like adding up the wrapping paper for the sides and the gift wrap for the triangles.

And there you have it. You’ve mastered the art of finding the surface area of a right triangular prism. Next time you’re stuck, remember this formula explained above.

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