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 feet

Explanation:

Step1: Identify the faces of the prism

A triangular prism has 2 triangular faces and 3 rectangular faces. The triangular faces have sides 5 ft, 12 ft, 13 ft (a right - triangle since \(5^{2}+12^{2}=13^{2}\)). The rectangular faces have dimensions: one with 5 ft and 25 ft, one with 12 ft and 25 ft, and one with 13 ft and 25 ft.

Step2: Calculate the area of the triangular faces

The area of a triangle with base \(b\) and height \(h\) is \(A_{triangle}=\frac{1}{2}bh\). For a right - triangle with legs 5 ft and 12 ft, \(A_{triangle}=\frac{1}{2}\times5\times12 = 30\) square feet. Since there are 2 triangular faces, the total area of the triangular faces is \(2\times30=60\) square feet.

Step3: Calculate the area of the rectangular faces

The area of the first rectangular face with dimensions 5 ft and 25 ft is \(A_{1}=5\times25 = 125\) square feet.
The area of the second rectangular face with dimensions 12 ft and 25 ft is \(A_{2}=12\times25=300\) square feet.
The area of the third rectangular face with dimensions 13 ft and 25 ft is \(A_{3}=13\times25 = 325\) square feet.
The total area of the rectangular faces is \(A_{rectangles}=125 + 300+325=750\) square feet.

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. So \(SA=60 + 750=810\) square feet.

Answer:

810