Question

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

Explanation:

Step1: Find area of triangular faces

The triangular faces have base $b = 9$ mm and height $h=12$ mm. Area of a triangle formula is $A_{\triangle}=\frac{1}{2}bh$. So $A_{\triangle}=\frac{1}{2}\times9\times12 = 54$ square - mm. Since there are 2 triangular faces, the total area of triangular faces is $2\times54 = 108$ square - mm.

Step2: Find area of rectangular faces

There are three rectangular faces.

• First rectangle with dimensions $60$ mm and $9$ mm: $A_1 = 60\times9=540$ square - mm.
• Second rectangle with dimensions $60$ mm and $12$ mm: $A_2 = 60\times12 = 720$ square - mm.
• Third rectangle with dimensions $60$ mm and $15$ mm: $A_3 = 60\times15=900$ square - mm.

Step3: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of the triangular and rectangular faces. $A=108 + 540+720 + 900=2268$ square - mm.

Answer:

2268