Answer:
149.28 m²
Explanation:
You want the surface area of the trapezoidal prism shown in the attached figure.
Area
The surface area of the prism is the sum of the two trapezoidal base areas and the lateral area.
Trapezoid
The area of each trapezoid base is ...
A = (1/2)(b1 +b2)h = (1/2)(4 m +6 m)(6 m) = 30 m²
The total area of the two trapezoidal bases is ...
total base area = 2×30 m² = 60 m²
Lateral area
The lateral area of the prism is the product of the perimeter of the base and the height of the prism:
LA = Ph
LA = (6 m + 4 m + 2 m + 6.32 m + 4 m)(4 m) = 89.28 m²
Total area
The sum of the areas of the bases and the sides is ...
surface area = 60 m² +89.28 m² = 149.28 m²
The surface area of the composite object is about 149.28 m².
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