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Formula for Surface Area of a Triangular Prism

TopA solid object which has two ends and also has a flat surface is known as a prism. Now, we will see the formula for surface area of a triangular prism.

The surface area of a triangular prism = 2B + PH.
Surface area = BH + (s1 + s2 + s3) H.
Where, ‘B’ is the area of the base, ‘p’ is the perimeter of the base, ‘h’ is the height of a triangular prism, and s1, s2, s3 are the sides of a triangle.

Now, we will see how to find the surface area of a triangular prism.

For finding the surface area of a triangular prism, we have to follow the steps given below:

Step 1: First, we have to find the base value of a triangular prism.
Step 2: Then, we have to find the perimeter of a triangular prism. We know that the perimeter of a triangular prism is the sum of all sides of the prism.
Step 3: Now, we have to find the height of the triangular prism.
Step 4: When we put all the values in the given surface formula, we get the surface area of a triangular prism.

Now, let us consider an example to find the surface area of a triangular prism.

Example:

Find the surface area of a triangular prism, where the triangle sides are (5 inch, 6 inch, 7 inch) and height of a prism is 12 inch.

Solution:

The surface area of a triangular prism = BH + (s1 + s2 + s3) H.
Step 1: We have to find the perimeter of a triangular prism as follows:
We know that the perimeter of a prism is the sum of all the three sides of a prism.
The three sides are 5 inch, 6 inch, 7 inch.
So, the perimeter = (5 + 6 + 7) inch.
Perimeter = 18 inch.
Triangle base = 5 inch.
Triangle height = 6 inch.
Height = 12 inch.

Step 2: Now, put the value in the surface area formula as follows:
The surface area of a triangular prism = BH + (s1 + s2 + s3) H.
Surface area = 5(6) + 18 x 12.
Surface area = 30 + 216.
Surface area = 246 inch2
The surface area of a triangular prism is 246 inch2.