Question

ight triangular prism and its net are shown below. (all lengths are in centimeters.) (a) find the following side lengths for the net. ( a = 2 mathrm{cm} ) ( b = 8 mathrm{cm} ) ( c = 6 mathrm{cm} ) ( d = 10 mathrm{cm} ) (b) use the net to find the surface area of the prism.

Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a right - angled triangle is \(A=\frac{1}{2}\times base\times height\).
For the triangular faces of the prism, \(base = 6\) cm and \(height = 8\) cm.
The area of one triangular face \(=\frac{1}{2}\times6\times8=24\) \(cm^{2}\).
Since there are two triangular faces, the total area of the triangular faces \(=2\times24 = 48\) \(cm^{2}\).

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.
The areas of the rectangular faces:

• One with dimensions \(10\times2\): Area \(A_1=10\times2 = 20\) \(cm^{2}\)
• One with dimensions \(8\times2\): Area \(A_2=8\times2=16\) \(cm^{2}\)
• One with dimensions \(6\times2\): Area \(A_3=6\times2 = 12\) \(cm^{2}\)

The total area of the rectangular faces \(=20 + 16+12=48\) \(cm^{2}\)

Step3: Calculate the total surface area

The total surface area of the prism is the sum of the area of the triangular faces and the area of the rectangular faces.
Total surface area \(S=48 + 48=96\) \(cm^{2}\)

Answer:

The surface area of the prism is \(96\) \(cm^{2}\)