Question

the figure shows a net of a rectangular prism. area of rectangle a = l·w. which expression can be used to find the surface area of the prism? (20·8)+(20·3)+(8·3), 2(20·8·3), 2(20·8)+2(20·3)+2(8·3), 20·8·3

Explanation:

Step1: Identify the faces of the rectangular - prism

A rectangular prism has 6 faces. In a net of a rectangular prism, we have three pairs of congruent faces. The dimensions of the faces are: length \(l = 20\) cm, width \(w = 8\) cm, and height \(h=3\) cm.

Step2: Recall the formula for the surface - area of a rectangular prism

The surface - area formula of a rectangular prism is \(SA = 2(lw+lh + wh)\). This formula comes from adding the areas of all 6 faces. The areas of the three pairs of faces are \(lw\), \(lh\), and \(wh\) respectively, and we multiply each by 2 since there are two of each type of face.

Step3: Substitute the values

Here, \(l = 20\), \(w = 8\), and \(h = 3\). The areas of the three pairs of faces are:

• The first pair with area \(lw\): \(20\times8\), and there are 2 such faces, so the total area for this pair is \(2(20\times8)\).
• The second pair with area \(lh\): \(20\times3\), and there are 2 such faces, so the total area for this pair is \(2(20\times3)\).
• The third pair with area \(wh\): \(8\times3\), and there are 2 such faces, so the total area for this pair is \(2(8\times3)\).

The surface - area formula becomes \(SA=2(20\times8)+2(20\times3)+2(8\times3)\).

Answer:

\(2(20\times8)+2(20\times3)+2(8\times3)\)