Question

using a net to find the surface area of a rectangular prism
(a) find the following side lengths for the net.
a = □ yd
b = □ yd
c = □ yd
d = □ yd

Explanation:

Step1: Identify the side lengths of the rectangular prism

A rectangular prism has 3 pairs of opposite faces. In the given rectangular prism, the dimensions are \(2\) yd, \(5\) yd, and \(9\) yd (assuming the height \(B = 9\) yd from the standard problem - usually when the base has sides \(2\) and \(5\)).

• For the net of a rectangular prism, the length \(A\) is the height of the prism. If we consider the formula for the surface area of a rectangular prism \(S = 2(lw+lh + wh)\) where \(l = 5\), \(w=2\), and \(h\) is the other dimension. In the net, the side \(A\) corresponds to the height of the prism. Let's assume the height of the prism (the dimension perpendicular to the base with sides \(2\) and \(5\)) is \(9\) (a common value if we assume the problem is following standard textbook problems where the three dimensions are \(2\), \(5\), and \(9\)). So \(A = 9\) yd.
• The side \(B\) is one of the smaller - side lengths of the rectangles in the net. Since the base of the prism has sides \(2\) and \(5\), and considering the structure of the net (where \(B\) is adjacent to the height - like part of the lateral face), \(B = 2\) yd.
• The side \(C\) is equal to the length of the base of the prism. So \(C = 5\) yd.
• The side \(D\) is equal to the width of the base of the prism. So \(D = 2\) yd.

Answer:

\(A = 9\) yd, \(B = 2\) yd, \(C = 5\) yd, \(D = 2\) yd