Question

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

Answer 1

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

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 * 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.