Question

1. determine the surface area of each composite object. what effect does the overlap have on the calculation of the surface area? a) 1 cm 2 cm 1 cm 2 cm 3 cm 5 cm

Explanation:

Step1: Calculate the surface area of the larger rectangular prism

The formula for the surface area of a rectangular prism is \(S = 2(lw+lh + wh)\). For the larger prism with \(l = 5\space cm\), \(w=3\space cm\), \(h = 2\space cm\):

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Step2: Calculate the surface area of the smaller rectangular prism

For the smaller prism with \(l = 2\space cm\), \(w = 1\space cm\), \(h=1\space cm\) (assuming height is same as width for the small - prism from the overlap context):

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Step3: Calculate the area of the overlapping region

The overlapping region is a rectangle with \(l = 2\space cm\) and \(w = 1\space cm\). The area of one - side of the overlap is \(A=2\times1 = 2\space cm^{2}\). Since the overlap hides two faces (one from each prism), we subtract \(2A\) from \(S_{1}+S_{2}\)

Step4: Calculate the surface area of the composite object

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The overlap reduces the total surface area. When two objects are joined, the area of the overlapping region (two times the area of the common face, because each object loses a face at the overlap) is subtracted from the sum of the surface areas of the individual objects.

Answer:

The surface area of the composite object is \(68\space cm^{2}\). The overlap reduces the total surface area by \(4\space cm^{2}\) (since two faces of area \(2\space cm^{2}\) each are covered).