Question

what is the surface area of the box, in square inches, that grayson decorates? answer

Explanation:

Step1: Identify the dimensions of the box's faces

The box has 6 faces. There are two faces with dimensions 12 in × 13 in, two faces with dimensions 12 in × 11 in, and two faces with dimensions 11 in × 13 in.

Step2: Calculate the area of each - type of face

For the 12 in × 13 in faces:
The area of one 12 in × 13 in face is $A_1=12\times13 = 156$ square - inches. The total area of the two 12 in × 13 in faces is $2\times156 = 312$ square - inches.
For the 12 in × 11 in faces:
The area of one 12 in × 11 in face is $A_2=12\times11 = 132$ square - inches. The total area of the two 12 in × 11 in faces is $2\times132 = 264$ square - inches.
For the 11 in × 13 in faces:
The area of one 11 in × 13 in face is $A_3=11\times13 = 143$ square - inches. The total area of the two 11 in × 13 in faces is $2\times143 = 286$ square - inches.

Step3: Calculate the total surface area

The total surface area $S$ of the box is the sum of the areas of all 6 faces.
$S=312 + 264+286=862$ square - inches.

Answer:

862