a triangular prism is shown below. which diagram is a net for this prism? what is the surface area of the…

Explanation:

Step1: Identify the net

A triangular - prism net has two triangular faces and three rectangular faces. By comparing the dimensions of the given prism (sides of triangles and lengths of rectangles), we can identify the correct net. The first net is the correct one as it has the right - sized triangles and rectangles corresponding to the prism.

Step2: Calculate surface area

1. Area of triangular faces:
   • The formula for the area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces of the prism, $b = 40$ in and $h = 15$ in. So, $A_{triangle}=\frac{1}{2}\times40\times15=300$ square inches. Since there are 2 triangular faces, the total area of triangular faces is $2\times300 = 600$ square inches.
2. Area of rectangular faces:
   • First rectangle: with dimensions $9$ in and $25$ in, $A_1=9\times25 = 225$ square inches.
   • Second rectangle: with dimensions $40$ in and $25$ in, $A_2=40\times25=1000$ square inches.
   • Third rectangle: with dimensions $15$ in and $25$ in, $A_3=15\times25 = 375$ square inches.
   • The total area of rectangular faces is $A_{rectangles}=225 + 1000+375=1600$ square inches.
3. Total surface area:
   • The surface area of the prism $A = A_{triangles}+A_{rectangles}=600 + 1600=2200$ square inches.

Answer:

The correct net is the first one shown. The surface area of the triangular prism is 2200 square inches.