# How to Work Out the Surface Area of a Triangular Prism (Right Angled and Isosceles)

The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and 2 being triangular.

The area of the rectangular faces can be found by multiply the base and height lengths together. The area of the triangular faces can be found by multiplying the base and height and dividing by 2. Once all these faces have been calculated the surface area can be found by adding up all of these faces.

**Example 1**

Work out the surface area of this triangular prism.

Let’s begin with the triangular faces. Both faces have the same area as it’s a prism! Just multiply the base and height and divide the answer by 2:

Area of triangular faces = (base × height) ÷ 2

Area of triangular faces = (3 × 4) ÷ 2 = 6 cm²

Next work out the area of the rectangular faces. Each face is a different sized rectangle, and can be calculated by multiply the base by the height:

Area of sloping rectangular face = 5 × 11 = 55 cm²

Area of back rectangular face = 3 × 11 = 33 cm²

Area of bottom rectangular face = 4 × 11 = 44 cm²

All you need to do is total all these areas:

6 + 6 + 55 + 33 + 44 = 144 cm²

So the total area of this triangular prism is 144 cm²

Let’s look at one more example of calculating the surface area of a triangular prism.

**Example 2**

Work out the surface area of this isosceles triangular prism.

Again, start by working out the area of the triangular faces. Just multiply the base and height and divide the answer by 2 (make sure you use the vertical height):

Area of triangular faces = (base × height) ÷ 2

Area of triangular faces = (4 × 6) ÷ 2 = 12 cm²

Next work out the area of the rectangular faces. Two of the faces are the same and the other is different:

Area of sloping rectangular faces = 7 × 12 = 84 cm²

Area of bottom rectangular face = 4 × 12 = 48 cm²

All you need to do now is total all of these areas:

12 + 12 + 84 + 84 + 48 = 240 cm²

So the total area of this isosceles triangular prism is 240 cm²

If you are finding this difficult then check out this help page on the surface area of a rectangular prism:

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