Question

What is the total surface area of the box formed by the pattern below

Answer 1

Answer:

The total surface area of the box is 224 square inches.

Step-by-step explanation:

The box pattern is shown in the image attached.

The total surface is the sum of the area of each section of the figure, which is formed by 4 equal rectangles and 2 equal squares. Rectangles have dimensions of 12 inches by 4 inches, and squares have 4 inches per side.

So, the total surface would be

$S_{total}=S_{squares} +S_{rectangles}\\ S_{total}=2(4in)^{2} +4(12in \times 4 in)\\ S_{total}=2(16in^{2})+4(48in^{2} ) \\ S_{total}=32in^{2}+192in^{2}\\ S_{total}=224in^{2}$

Therefore, the total surface area of the box is 224 square inches.