Answer:
The total surface area of the shape is 376 square inches.
Bonus: the volume is 240 cubic inches.
Step-by-step explanation:
I'm not going to draw this for you, but to get the area, you just need to add up the area of the 6 rectangles.
First though, you need to know what they are. This is easier than it may seem though. You just need to remember that this will be folded into a rectangular box. You are given three side lengths, which is all that is needed for a box.
That is to say, you're given the width, height and length of this box. It's 10x8x6 inches.
so if you take every possible pairing of those numbers:
10x8
10x6
8x6
you have the area of all of the shapes. The only catch is that there are two of each size. Front and back are the same size, left and right are, and so are top and bottom.
So the total area of the shape is:
(front and back) + (left and right) + (top and bottom)
= (2 × 10 × 8) + (2 × 10 × 6) + (2 × 8 × 6)
= 160 + 120 + 96
= 376
Or rather, 376 square inches.
Bonus: the volume is much easier, being just 10 × 8 × 6, or 240 cubic inches.
