The area of the wedge = 12 + 18 + 24 + 30 = 84 ft².
The surface area of a wedge = the area of each net that makes up the wedge.
Let's find the area of each net (3 rectangles and 2 triangles) in the diagram attached below:
Area of the two identical triangles:
Area of triangle = 2[1/2(base × height)] = 2[1/2(4 × 3)] = 12 ft².
Area of Rectangle 1:
Area = length × width = 6 × 3 = 18 ft²
Area of Rectangle 2:
Area = length × width = 6 × 4 = 24 ft²
Area of Rectangle 3:
Area = length × width = 6 × 5 = 30 ft²
Therefore, area of the wedge = 12 + 18 + 24 + 30 = 84 ft².
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