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

Explanation:

Step1: Identify the net of the triangular - prism

A triangular prism has two triangular faces and three rectangular faces. The correct net should have two congruent triangles and three rectangles that can be folded to form the prism. The first diagram is the correct net as it has two right - angled triangles with sides 3 cm, 4 cm and rectangles with appropriate dimensions to form the given prism.

Step2: Calculate the area of the triangular faces

The area of a right - angled triangle with base $b = 3$ cm and height $h = 4$ cm is $A_{triangle}=\frac{1}{2}\times b\times h$. $A_{triangle}=\frac{1}{2}\times3\times4 = 6$ square cm. Since there are 2 triangular faces, the total area of the triangular faces is $2\times6=12$ square cm.

Step3: Calculate the area of the rectangular faces

There are three rectangular faces:

• One rectangle with dimensions 3 cm and 16 cm, its area $A_1 = 3\times16=48$ square cm.
• One rectangle with dimensions 4 cm and 16 cm, its area $A_2 = 4\times16 = 64$ square cm.
• One rectangle with dimensions 5 cm and 16 cm, its area $A_3=5\times16 = 80$ square cm. The total area of the rectangular faces is $A_{rectangles}=48 + 64+80=192$ square cm.

Step4: Calculate the surface area of the prism

The surface area $A$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. $A=12 + 192=204$ square cm.

Answer:

204