Question

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

Answer 1

Answer:

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 $in^{2}$

Step-by-step 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 $in^{3}$.