Question

which diagram is a net for this prism? what is the surface area of the triangular prism? square feet

Explanation:

Step1: Identify prism parts

A triangular - prism net has 2 triangular faces and 3 rectangular faces.

Step2: Analyze given nets

The net on the left is the correct net for the given prism as it has the correct arrangement of the triangular base with dimensions 24 ft (base of triangle), 14 ft (height of triangle) and the rectangular lateral - faces with dimensions 25 ft, 10 ft etc.

Step3: Calculate surface area

1. Area of triangular faces:

The area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base = 24 ft and height = 14 ft. So, $A_{triangle}=\frac{1}{2}\times24\times14 = 168$ square feet. Since there are 2 triangular faces, the total area of triangular faces is $2\times168 = 336$ square feet.

1. Area of rectangular faces:

• There are three rectangular faces.
• One rectangle has dimensions 25 ft and 10 ft, so its area $A_1 = 25\times10=250$ square feet.
• Another rectangle has dimensions 25 ft and 14 ft, so its area $A_2 = 25\times14 = 350$ square feet.
• The third rectangle has dimensions 25 ft and 24 ft, so its area $A_3=25\times24 = 600$ square feet.

1. Total surface area:

The total surface area $A = 336+250 + 350+600=1536$ square feet.

Answer:

1536