Question

Use the diagram below to answer parts B, and C.

5 in
5 in
4.3 in
14 in
5 in
Part B: What is the volume of the triangular prism?
Volume =
in3
Part C: What is the surface area of the triangular prism?
in2
Surface Area =

Answer 1

The volume of the triangular prism in the diagram is:

• 105.5
  `in^(3)`

The surface area of the triangular prism in the diagram is:

• 10.75
  `in^(2)`

Explanation:

First, we're gonna calculate the surface area to obtain the volume, then, to calculate the area of a triangle (because the surface o a triangular prism is just a triangle), you can use the formula:

• Area of a triangle = (base * height) / 2

We have this data from the diagram, where the base of the triangles is 5 inches and, the height is 4.3 inches, replacing this in the formula:

• Area of a triangle = ( 5 in * 4.3 in) / 2
• Area of a triangle = ( 21.5
  `in^(2)`) / 2
• Area of a triangle = 10.75
  `in^(2)`

Now, we can calculate the volume of the triangular prism with the next formula:

• Volume of a triangular prism = surface area * depth

In the diagram, we can see the depth is 14 inches, then:

• Volume of a triangular prism = 10.75
  `in^(2)` * 14 in
• Volume of a triangular prism = 105.5
  `in^(3)`

How you can see with the calculations perfomed, the surface area is 10.75
`in^(2)` and the volume of that triangular prism is 105.5
`in^(3)`.