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: Identify the faces of the prism

The triangular prism has 2 triangular faces and 3 rectangular faces. The triangular faces have base - 8 mm and height - 3 mm, and the rectangular faces have dimensions: 12×5, 12×8, 12×5.

Step2: Calculate the area of the triangular faces

The area formula for a triangle is $A=\frac{1}{2}bh$. For $b = 8$ mm and $h=3$ mm, $A_{triangle}=\frac{1}{2}\times8\times3=12$ square - mm. The total area of the two triangular faces is $2\times12 = 24$ square - mm.

Step3: Calculate the area of the rectangular faces

The areas of the rectangular faces are:

• $A_1=12\times5 = 60$ square - mm
• $A_2=12\times8 = 96$ square - mm
• $A_3=12\times5 = 60$ square - mm

The total area of the rectangular faces is $60 + 96+60=216$ square - mm.

Step4: Calculate the surface area

The surface area $A$ of the triangular prism is the sum of the areas of the triangular and rectangular faces. $A = 24+216=240$ square - mm.

Answer:

240