Question

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

Explanation:

Step1: Identify the faces of the prism

The triangular - prism has 2 triangular faces and 3 rectangular faces.

Step2: Calculate the area of the triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces with $b = 24$ ft and $h=14$ ft, $A_{triangle}=\frac{1}{2}\times24\times14= 168$ square - feet. The total area of the 2 triangular faces is $2\times168 = 336$ square - feet.

Step3: Calculate the area of the rectangular faces

There are three rectangular faces:

• One with dimensions $25$ ft by $10$ ft, $A_1=25\times10 = 250$ square - feet.
• One with dimensions $25$ ft by $10$ ft, $A_2=25\times10 = 250$ square - feet.
• One with dimensions $25$ ft by $14$ ft, $A_3=25\times14 = 350$ square - feet.

The total area of the rectangular faces is $A_{rectangles}=250 + 250+350=850$ square - feet.

Step4: Calculate the surface area

The surface area $SA$ of the triangular prism is the sum of the areas of the triangular and rectangular faces. $SA=336 + 850=1186$ square - feet.

Answer:

1186 square feet