Answer:
(a) A = 10 ft; B = 2 ft; C = 5 ft; D = 2 ft
(b) 160 ft²
Explanation:
You want the dimensions of the net, and the total surface area, of the rectangular prism with dimensions 2 ft by 5 ft by 10 ft.
(a) Net
Th lengths marked B and D on the net are adjacent to the shortest sides, 2 ft. The length marked C on the net is the middle-length side, 5 ft. The length marked A on the net represents the longest side, 10 ft.
A = 10 ft; B = D = 2 ft; C = 5 ft
(b) Area
The area of the prism can be found by adding up the areas of the 6 rectangular faces. The formula for that can be simplified slightly to give ...
A = 2(LW +H(L +W))
A = 2(2·5 +10(2 +5)) = 2(10 +70) = 160 . . . . square feet
The surface area of the prism is 160 ft².
__
Additional comment
Effectively, the formula we used above is ...
Area = 2(BC +A(D+C)) . . . . . where A, B, C, D are the net dimensions
The is the sum of the areas of the top and bottom "wings" and the areas of the four rectangles between them. There are 2 of each size rectangle, so we factored that out. This formula minimizes the number of math operations required, and the number of times a dimension must be entered into the calculator.
<95141404393>