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 centimeters

Explanation:

Step1: Identify the faces of the prism

The triangular prism has 2 triangular faces and 3 rectangular faces. The triangular faces have base $b = 8$ cm and height $h=15$ cm, and the rectangular faces have dimensions: $40\times8$, $40\times15$, and $40\times17$.

Step2: Calculate the area of the triangular faces

The area formula for a triangle is $A_{\triangle}=\frac{1}{2}bh$. Substituting $b = 8$ cm and $h = 15$ cm, we get $A_{\triangle}=\frac{1}{2}\times8\times15=60$ square - cm. The total area of the 2 triangular faces is $2\times60 = 120$ square - cm.

Step3: Calculate the area of the rectangular faces

The area of the first rectangular face with dimensions $40\times8$ is $A_1=40\times8 = 320$ square - cm.
The area of the second rectangular face with dimensions $40\times15$ is $A_2=40\times15 = 600$ square - cm.
The area of the third rectangular face with dimensions $40\times17$ is $A_3=40\times17 = 680$ square - cm.
The total area of the rectangular faces is $A_{rect}=320 + 600+680=1600$ square - cm.

Step4: Calculate the total surface area

The total surface area $A$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So, $A=120 + 1600=1720$ square - cm.

Answer:

1720