Question

(a) find the following side lengths for the net.

a = 5 cm

b = 3 cm

c = 8 cm

d = 4 cm

(b) use the net to find the surface area of the prism.

Explanation:

Step1: Calculate the area of the two triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 4\) cm and \(h=3\) cm.

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The area of the two triangular bases is \(2\times A_{triangle}=2\times6 = 12\text{ cm}^2\)

Step2: Calculate the area of the three rectangular faces

• For the rectangle with sides \(A = 5\) cm and \(C=8\) cm: \(A_{1}=5\times8 = 40\text{ cm}^2\)
• For the rectangle with sides \(B = 3\) cm and \(C = 8\) cm: \(A_{2}=3\times8=24\text{ cm}^2\)
• For the rectangle with sides \(D = 4\) cm and \(C = 8\) cm: \(A_{3}=4\times8 = 32\text{ cm}^2\)

The sum of the areas of the three rectangular faces is \(A_{rectangles}=40 + 24+32=96\text{ cm}^2\)

Step3: Calculate the surface area of the prism

The surface area \(S\) of the prism is the sum of the areas of the triangular bases and the rectangular faces.

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Answer:

The surface area of the prism is \(108\text{ cm}^2\)