Question

A triangular prism and its dimensions are shown in the diagram. What is the total surface area of this triangular prism?

a = 13.8
b = 16.2
c = 4.6
d = 22.6

Answer 1

The Surface Area of the triangular prism is 316.48.

To find the total surface area of the triangular prism, we need to calculate the areas of each of its faces and then sum them up.

The surface area of a triangular prism is given by the formula:

`\[ \text{Surface Area} = 2(\text{Area of the triangular base}) + (\text{Perimeter of the triangular base}) * (\text{Height of the prism}) \]`

1. Area of the Triangular Base:

`\[ \text{Area} = (1)/(2) * b * c \]`

`\[ \text{Area} = (1)/(2) * 16.2 * 4.6 \]`

Area of the triangular base =37.26

2. Perimeter of the Triangular Base:

`\[ \text{Perimeter} = a + b + d \]`

`\[ \text{Perimeter of the Triangular Base} = 13.8 + 16.2 + 22.6 \]`

The perimeter of the triangular base= 52.6

3. Height of the Prism:

The height of the prism is c.

Substituting these values we get:

Surface Area =2 x 37.26+52.6 x 4.6

Surface Area= 74.52+ 241.96

Surface Area= 316.48

Therefore, the Surface Area of the triangular prism is 316.48.