Question

lengths are in centimeters.)
(a) find the following side lengths for the net.

a = 2 cm
b = 10 cm
c = 6 cm
d = 8 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 triangle is \(A=\frac{1}{2}bh\). For the right - angled triangle with \(b = 8\) and \(h=6\), the area of one triangular face is \(\frac{1}{2}\times8\times6=24\) \(cm^{2}\). Since there are 2 triangular faces, the total area of the triangular faces is \(2\times24 = 48\) \(cm^{2}\).

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• One rectangle has dimensions \(A = 2\) and \(B=10\), its area \(A_{1}=2\times10 = 20\) \(cm^{2}\).
• One rectangle has dimensions \(A = 2\) and \(C = 6\), its area \(A_{2}=2\times6=12\) \(cm^{2}\).
• One rectangle has dimensions \(A = 2\) and \(D = 8\), its area \(A_{3}=2\times8 = 16\) \(cm^{2}\).

The total area of the rectangular faces is \(A_{1}+A_{2}+A_{3}=20 + 12+16=48\) \(cm^{2}\).

Step3: Calculate the total surface area

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

Answer:

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