Question

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 - 15 cm and height - 8 cm, and the rectangular faces have dimensions: 40 cm×15 cm, 40 cm×8 cm, 40 cm×17 cm.

Step2: Calculate the area of the triangular faces

The area formula for a triangle is $A=\frac{1}{2}bh$. For each triangular face with $b = 15$ cm and $h = 8$ cm, $A_{triangle}=\frac{1}{2}\times15\times8=60$ square cm. The total area of the two triangular faces is $2\times60 = 120$ square cm.

Step3: Calculate the area of the rectangular faces

For the first rectangular face with dimensions 40 cm×15 cm, $A_1=40\times15 = 600$ square cm.
For the second rectangular face with dimensions 40 cm×8 cm, $A_2=40\times8=320$ square cm.
For the third rectangular face with dimensions 40 cm×17 cm, $A_3=40\times17 = 680$ square cm.
The total area of the rectangular faces is $A_{rectangles}=600 + 320+680=1600$ square cm.

Step4: Calculate the total surface area

The total surface area of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. $A_{total}=120 + 1600=1720$ square cm.

Answer:

1720