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 millimeters

Explanation:

Step1: Identify the faces of the prism

A triangular prism has 2 triangular faces and 3 rectangular faces. The triangular faces have sides 9 mm, 12 mm, 15 mm (a right - triangle since \(9^{2}+12^{2}=15^{2}\)), and the rectangular faces have dimensions: one with sides 9 mm and 60 mm, one with sides 12 mm and 60 mm, and one with sides 15 mm and 60 mm.

Step2: Calculate the area of the triangular faces

The area of a triangle is \(A=\frac{1}{2}bh\). For a right - triangle with base \(b = 9\) mm and height \(h = 12\) mm, \(A_{triangle}=\frac{1}{2}\times9\times12=54\) \(mm^{2}\). The total area of the two triangular faces is \(2\times54 = 108\) \(mm^{2}\).

Step3: Calculate the area of the rectangular faces

The area of the first rectangular face with sides 9 mm and 60 mm is \(A_{1}=9\times60 = 540\) \(mm^{2}\).
The area of the second rectangular face with sides 12 mm and 60 mm is \(A_{2}=12\times60=720\) \(mm^{2}\).
The area of the third rectangular face with sides 15 mm and 60 mm is \(A_{3}=15\times60 = 900\) \(mm^{2}\).

Step4: Calculate the total surface area

The total surface area \(A = A_{triangles}+A_{1}+A_{2}+A_{3}\).
\(A=108 + 540+720 + 900=2268\) \(mm^{2}\).

Answer:

2268