Answer:
294 cm²
Step-by-step explanation:
You want the total surface area of a trapezoidal prism as shown in the diagram.
Base area
The area of each trapezoidal base is given by ...
A = 1/2(b1 +b2)h
A = 1/2((7 cm +4 cm) +7 cm)(6 cm) = 54 cm²
Lateral area
The area of the 5 rectangular faces is the product of the perimeter of the trapezoid and the height of the prism.
LA = P·h
LA = (11 cm + 7 cm + 7 cm + 6 cm)(6 cm) = (31)(6) cm² = 186 cm²
Surface area
The surface area of the prism is the sum fo the areas of the 2 bases and the lateral area:
SA = 2·base area + LA
SA = 2(54 cm²) +186 cm² = 294 cm²
The curface area of the composite figure is 294 cm².
