Answer:
- see the attached for a net
- surface area: 355.5 in²
Step-by-step explanation:
Once you have drawn a net and labeled the dimensions, the area can be found any number of ways. I divided the net into two rectangles (red and blue) as shown and figured the are of each.
area of red rectangle = 4.5·27 = 121.5 . . . . square inches
area of blue rectangle = 19.5·12 = 234 . . . . square inches
Then the total surface area of the box is ...
total area = red area + blue area = 121.5 in² + 234 in² = 355.5 in²
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You can also figure the surface area SA using the formula ...
SA = 2(LW +H(L+W))
Filling in the numbers shown on the diagram, you have ...
SA = 2(12·4.5 +7.5(12+4.5)) = 355.5 . . . . square inches
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In the figure, the top, front, and right side are shown. The bottom corner where the front and right side meet can be called point A. Then, in clockwise order, the points around the right side face can be called B, C, D, and back to A (called E on the net).
The point at the bottom left end of the front can be called point F. Then the one above it can be called G, and the point where the top, back, and left side meet can be called H. The hidden corner where the dotted lines come together can be called point I, and point J on the net will be another name for point F. Other doubly-named points on the net are (H, M), (G, N), (C, K), and (B, L).
If it helps, you can cut the net from a piece of paper, fold it on the lines, and match the doubly-named points to make the box. (I recommend you do an exercise like this at least once so you can gain a physical understanding of how the net matches the box surface.)
