Question

a rectangular prism and its net are shown below. (all lengths are in feet.) (a) find the following side lengths for the net. ( a=square mathrm{ft} ) ( b=square mathrm{ft} ) ( c=square mathrm{ft} ) ( d=square mathrm{ft} ) (b) use the net to find the surface area of the prism. ( square mathrm{ft}^{2} )

Explanation:

Step1: Identify the side lengths from the rectangular prism

A rectangular prism has 3 pairs of opposite faces. In the given prism, the dimensions are \(l = 10\) ft (length), \(w=6\) ft (width), \(h = 2\) ft (height).

• For the net of a rectangular prism, \(A\) is the sum of two different side - lengths. \(A=10 + 2=12\) ft.
• \(B\) is the length of the longest side of the base of the prism, so \(B = 10\) ft.
• \(C\) is the height of the prism, so \(C=2\) ft.
• \(D\) is the width of the prism, so \(D = 6\) ft.

Step2: Calculate the surface area of the rectangular prism

The formula for the surface area of a rectangular prism \(S=2(lw+lh + wh)\)
Substitute \(l = 10\), \(w = 6\), \(h=2\) into the formula:

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Answer:

A = 12 ft, B = 10 ft, C = 2 ft, D = 6 ft, Surface area = 184 ft²