How to Find Surface Area of Triangular Prism?

Surface area of a triangular prism is the sum of the areas of all its faces. A triangular prism is a shape with two identical triangular faces and three rectangular faces connecting them. It has 6 corners, 9 edges, and 5 faces in total.

In this article, we’ll explore about how to find the total surface area of a triangular prism, including the formula and some examples to understand it better.

What is Total Surface Area of Triangular Prism?

Total surface area of a triangular prism refers to the combined area of all its faces. A triangular prism has two triangular faces and three rectangular faces. The rectangular faces are known as the lateral faces, while the triangular ones are called bases. If you position the bases horizontally, they become the top and bottom faces of the prism. Surface area is measured in square units such as square meters (m²), square centimetres (cm²), square inches (in²), or square feet (ft²).

Surface Area of Triangular Prism Formula

Surface area of a triangular prism is defined as the sum of the area of its five faces. To calculate the surface area, we need the values of the base, length, and height of the triangular prism. Its formula equals the sum of two times the base area and three times the product of the base and length of the prism. Its unit of measurement is meter square (sq. m).

A = b.h + 3l.b

where,

• b is Triangular Base
• h is Height
• l is Length of Prism

Formulas for finding the surface area of a Triangular Prism:

Aspect of Surface Area	Formula
Total Surface Area	2×(Area of Base) + Perimeter of Base×Height of Prism
Area of a Triangular Base	1/2×Base×Height
Perimeter of Base	Sum of Lengths of All Sides
Lateral Surface Area	Perimeter of Base×Height of Prism

These formulas provide various ways to calculate different aspects of the surface area of a triangular prism.

How to Find Surface Area of a Triangular Prism?

To find the surface area of a right triangular prism, follow these steps:

Step 1: Calculate the area of the two triangular bases by multiplying their base by their height. This gives you the area of one triangle. Since there are two congruent triangles, multiply this area by 2.

Step 2: Determine the perimeter of one of the triangular bases. Add up the lengths of all three sides.

Step 3: Multiply the perimeter of the base by the height of the prism. This gives you the lateral surface area.

Step 4: Add the areas of the two triangular bases and the lateral surface area to find the total surface area of the right triangular prism.

Let’s take an example to understand how we can calculate the surface area of a triangular prism.

Example: Calculate the surface area of a triangular prism of base 5 m, height 10 m and length 15 m.

Step 1: Note the dimensions of the triangular prism. In this example, the length of the base is 5 m, height is 10 m and length is 15 m.

Step 2: We know that the surface area of a triangular prism is equal to (bh + 3bl). Substitute the given values of base, height and length in the formula.

Step 3: So, the surface area of triangular prism is calculated as, A = 5 (10) + 3 (5) (15) = 275 sq. m

Sample Problems on the Surface Area of a Triangular Prism

Problem 1: Calculate the surface area of a triangular prism of base 6 m, height 3 m, and length 7 m. 

Solution:

We have,

• b = 6
• h = 3
• l = 7

Using formula we get,

A = bh + 3bl

= 6 (3) + 3 (6) (7)

= 144 sq. m

Problem 2: Calculate the surface area of a triangular prism of base 2 m, height 4 m, and length 6 m.

Solution:

We have,

• b = 2
• h = 4
• l = 6

Using formula we get,

A = bh + 3bl

= 2 (4) + 3 (2) (6)

= 44 sq. m

Problem 3: Calculate the surface area of a triangular prism of base 4 m, the height of 9 m, and length of 7 m.

Solution:

We have,

• b = 4
• h = 9
• l = 7

Using formula we get,

A = bh + 3bl

= 4 (9) + 3 (4) (7)

= 120 sq. m

Problem 4: Calculate the length of the triangular prism if its base is 4 m, height is 9 m and area is 198 sq. m.

Solution:

We have, 

• b = 6
• h = 9
• A = 198

Using the formula we get,

A = bh + 3bl

=> 198 = 6 (9) + 3 (6) (l)

=> 198 = 54 + 18l

=> 18l = 144

=> l = 8 m

Problem 5: Calculate the length of the triangular prism if its base is 5 m, height is 10 m and area is 180 sq. m.

Solution:

We have,

• b = 5
• h = 10
• A = 180

Using the formula we get,

A = bh + 3bl

=> 180 = 5 (10) + 3 (5) (l)

=> 180 = 54 + 15l

=> 15l = 126

=> l = 8.4 m

Problem 6: Calculate the height of the triangular prism if its base is 12 m, length is 14 m and area is 700 sq. m.

Solution:

We have,

• b = 12
• l = 14
• A = 700

Using the formula we get,

A = bh + 3bl

=> 700 = 12 (h) + 3 (12) (14)

=> 700 = 12h + 504

=> 12h = 196

=> h = 16.33 m

Problem 7: Calculate the height of the triangular prism if its base is 8 m, length is 14 m and area is 408 sq. m.

Solution:

We have,

• b = 8
• l = 14
• A = 408

Using the formula we get,

A = bh + 3bl

=> 408 = 8 (h) + 3 (8) (14)

=> 408 = 8h + 336

=> 8h = 72

=> h = 9 m

Frequently Asked Questions

What is a Triangular Prism, and how is its Surface Area Calculated?

A triangular prism is a three-dimensional shape with two congruent triangular bases and three rectangular faces. Its surface area is found by calculating the area of the triangular bases and the lateral faces, then summing them up.

What are Steps to find Surface Area of a Triangular Prism?

Steps to find Surface Area of a Triangular Prism are:

• Finding the area of the triangular bases.
• Calculating the perimeter of the base.
• Determining the lateral surface area, and finally.
• Adding all these values together to get the total surface area.

How to Calculate Area of Triangular Bases of a Triangular Prism?

Area of each triangular base can be found using the formula: 0.5 * base * height, where the base and height are the dimensions of the triangle.

What is the lateral surface area of a triangular prism?

Lateral surface area is the combined area of the three rectangular faces of the prism. It is calculated by multiplying the perimeter of the triangular base by the height of the prism.

Are there any shortcuts or tricks to simplify finding the surface area of a triangular prism?

One method is to break down the prism into its individual components (triangular bases and rectangular faces) and calculate their areas separately. Another approach is to visualize the prism as a net to better understand its surface area.

Can you provide an example of finding the surface area of a triangular prism?

We have a triangular prism with a base length of 6 cm, height of 8 cm, and prism height of 10 cm. We can calculate the surface area by finding the areas of the triangular bases 1/2× (6 × 8 × 2) and the lateral faces ((6 + 6 + 8) × 10) and then adding them together.