Question

olivia has a shoe box in the shape of a rectangular prism. she decorates 4 faces of the box, leaving the top and the bottom without decorations. the unshaded parts of the model and the diagram below show the parts that she decorates. what is the total area that olivia decorates?

Explanation:

Step1: Calculate the area of the two larger decorated faces

The two larger decorated faces have dimensions \(11\) in (length) and \(5\) in (height). The area of a rectangle is \(A = l\times h\). For one such face, \(A_1=11\times5 = 55\) square inches. For two faces, \(A_{1 - total}=2\times11\times5=110\) square inches.

Step2: Calculate the area of the two smaller decorated faces

The two smaller decorated faces have dimensions \(8\) in (length) and \(5\) in (height). The area of a rectangle is \(A = l\times h\). For one such face, \(A_2 = 8\times5=40\) square inches. For two faces, \(A_{2 - total}=2\times8\times5 = 80\) square inches.

Step3: Calculate the total decorated area

The total decorated area \(A=A_{1 - total}+A_{2 - total}\). Substitute the values: \(A=(2\times11\times5)+(2\times8\times5)=110 + 80=190\) square inches.

Answer:

\(190\) square inches