Answer:
- A = 2 mm
- B = 12 mm
- C = 5 mm
- D = 13 mm
- Area = 120 mm²
Explanation:
You want the dimensions of the net, and the total surface area of the triangular prism shown.
Net dimensions
A is the distance between the triangular bases, 2 mm.
B is the length of the long leg of the right triangle, 12 mm.
C is the length of the short leg of the right triangle, 5 mm.
D is the length of the hypotenuse of the right triangle, 13 mm.
Area
The total area is found by adding the areas of the parts of the net.
The two triangles together form a rectangle 5 mm by 12 mm, so their combined area is ...
A = LW = (5 mm)(12 mm) = 60 mm²
The three rectangles have a total length of 12 + 5 + 13 = 30 mm, and a width of 2 mm, so their total area is ...
A = LW = (30 mm)(2 mm) = 60 mm²
The total surface area of the prism is the sum of these:
60 mm² + 60 mm² = 120 mm²
The net dimensions are A=2, B=12, C=5, D=13, and the area is 120 mm².
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