which diagram is a net for this prism? what is the surface area of the triangular prism?

Explanation:

Step1: Identify the faces of the prism

The triangular - prism has 2 triangular faces and 3 rectangular faces. The triangular faces have base $b = 6$ in and height $h = 8$ in. The rectangular faces have dimensions: one with dimensions $6\times10$, one with dimensions $8\times10$, and one with dimensions $10\times10$.

Step2: Calculate the area of the triangular faces

The area of a triangle is $A_{\triangle}=\frac{1}{2}bh$. $A_{\triangle}=\frac{1}{2}\times6\times8 = 24$ square - inches. Since there are 2 triangular faces, the total area of the triangular faces is $2\times24 = 48$ square - inches.

Step3: Calculate the area of the rectangular faces

The area of the first rectangular face with dimensions $6\times10$ is $A_1 = 6\times10=60$ square - inches. The area of the second rectangular face with dimensions $8\times10$ is $A_2 = 8\times10 = 80$ square - inches. The area of the third rectangular face with dimensions $10\times10$ is $A_3 = 10\times10 = 100$ square - inches. The total area of the rectangular faces is $A_{rect}=60 + 80+100=240$ square - inches.

Step4: Calculate the surface area

The surface area $SA$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. $SA=48 + 240=288$ square - inches.

Answer:

288 square - inches