Surface Area of a Triangular Prism Formula | List of Surface Area of a Triangular Prism Formula You Should Know - BYJUS

# Surface Area of a Triangular Prism Formula

A polyhedron with three rectangular sides and two triangular bases is called a triangular prism. In this article, we will learn about the formula to find the surface area of a triangular prism along with solving a few examples to provide a better understanding about the surface area of a triangular prism....Read MoreRead Less

### What is the Formula for the Surface Area of a Triangular Prism?

A triangular prism is a three-dimensional shape with two triangular faces and three rectangular faces. The rectangular faces are known as the lateral faces and the triangular faces are the bases of the prism. The surface area of a triangular prism is calculated by adding up the area of the lateral faces and the triangular bases. Here is the formula for the surface area of a triangular prism.

Surface area of a triangular prism = bh + (a + b + c)H Let’s see what each term refers to:

‘a’, ‘b’, and ‘c’ are the side lengths of the triangular bases.

‘b’ and ‘h’ are the base and height of the triangular faces.

H is the height of the triangular prism.

### Rapid Recall Surface area of a triangular prism = bh + (a + b + c)H

### Solved Examples

Example 1:

Find the surface area of the triangular prism with the measurements seen in the image. Solution:

From the image, we can observe that the side lengths of the triangle are a = 5 cm, b = 6 cm and c = 5 cm.

The base and height of the triangular faces are b = 6 cm and h = 4 cm.

The height of the triangular prism is H = 15 cm

We can find the surface area of the triangular prism by applying the formula,

Surface area of a triangular prism = bh + (a + b + c)H

= 6 $$\times$$ 4 + (5 + 6 + 5) $$\times$$ 15   [Substitute the value]

= 24 + (16) $$\times$$ 15                   [Apply PEMDAS rule]

= 24 + 240                           [Multiply]

= 264 $$cm^2$$

Hence, the surface area of a triangular prism is 264 square centimeters.

Example 2:

Cathy recently purchased a new triangular kaleidoscope in which the sides are 9 cm long. The surface area of the kaleidoscope is 576 $$cm^2$$, and its base height is 7.8 cm. Find the height of the kaleidoscope. Solution:

As stated, the length of each side of the kaleidoscope is 7.8 cm.

That is, a = b = c = 9 cm.

It is mentioned that the surface area of the kaleidoscope is 576 $$cm^2$$ and the base height is 7.8 cm.

Since the kaleidoscope is in the shape of a triangular prism, we can use the formula for the surface area to find its height.

So,

Surface area of a triangular prism = bh + (a + b + c)H

576 = 9 $$\times$$ 7.8 + (9 + 9 + 9)H   [Substitute the value]

576 = 70.2 + (27)H                   [Apply PEMDAS rule]

576 – 70.2 = (27)H                   [Subtract 36 from both the sides]

505.8 = (27)H

$$\frac{505.8}{27}$$ = H                                  [Divide both sides by 27]

18.73 = H

Hence, the height of Cathy’s kaleidoscope is 18.73 cm.

Example 3:

Adam and Mac have set up a tent while they are on vacation. The image gives you the dimensions of the tent. How much cloth is used for a tent? Solution:

In the image, all the sides of the triangular faces of the tents are a = b = 5 ft and c = 8 ft

The height of a triangular face is 3 ft and the total length of the tent is 6 ft. So, to find the quantity of cloth used for a tent we add the area of two triangular faces and two rectangular faces.

Area of cloth required = $$2\times \frac{1}{2}$$ bh + (a + b)H

= $$2\times \frac{1}{2}\times 8 \times 3+(5+5)\times 6$$                    [Substitute the value]

= 24 + 10 $$\times$$ 6                                                [Apply PEMDAS rule]

= 24 + 60                                                        [Multiply]

= 84 $$ft^2$$                                                           [Add]

Therefore, 84 square feet of cloth is required for a tent.