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 decorated. what is the total area that olivia decorates? 190 square inches, 440 square inches, 300 square inches, 280 square inches

Explanation:

Step1: Identify the dimensions of the box

The box has dimensions length $l = 11$ in, width $w=5$ in and height $h = 8$ in.

Step2: Determine the 4 faces she decorated

She decorated 4 faces, which are two faces with dimensions $11\times8$ and two faces with dimensions $5\times8$.

Step3: Calculate the area of the $11\times8$ faces

The area of one $11\times8$ face is $A_1=11\times8 = 88$ square - inches. The area of two $11\times8$ faces is $2\times A_1=2\times88 = 176$ square - inches.

Step4: Calculate the area of the $5\times8$ faces

The area of one $5\times8$ face is $A_2 = 5\times8=40$ square - inches. The area of two $5\times8$ faces is $2\times A_2=2\times40 = 80$ square - inches.

Step5: Calculate the total decorated area

The total area of the 4 decorated faces is $A=176 + 80=256$ square - inches.

Answer:

256 square inches