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

Explanation:

Step1: Analyze the triangular - prism structure

A triangular prism has two triangular faces and three rectangular faces. The triangular faces have side - lengths 13 ft, 13 ft, and 10 ft, and the height of the prism is 14 ft.

Step2: Calculate the area of the triangular faces

The area of a triangle with sides (a = 13), (b = 13), (c = 10) can be found using Heron's formula. First, the semi - perimeter (s=\frac{a + b + c}{2}=\frac{13+13 + 10}{2}=\frac{36}{2}=18) ft. The area of the triangle (A_{triangle}=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{18(18 - 13)(18 - 13)(18 - 10)}=\sqrt{18\times5\times5\times8}=\sqrt{3600}=60) square feet. Since there are 2 triangular faces, the total area of the triangular faces is (2\times60 = 120) square feet.

Step3: Calculate the area of the rectangular faces

There are three rectangular faces. One has dimensions (10\times14), another has dimensions (13\times14), and the third has dimensions (13\times14). The area of the (10\times14) rectangle is (A_{1}=10\times14 = 140) square feet. The area of each of the (13\times14) rectangles is (A_{2}=13\times14 = 182) square feet, and the total area of the two (13\times14) rectangles is (2\times182=364) square feet.

Step4: Calculate the total surface area

The total surface area (A = 120+140 + 364=624) square feet.

Answer:

624