Answer:
2064 cm²
Step-by-step explanation:
You want the surface area of a prism that is 30 cm between bases that are trapezoids with parallel sides 27 cm and 6 cm that are 8 cm apart, and slant sides that are 10 cm and 17 cm.
Base area
The area of each trapezoidal base is ...
A = 1/2(b1 +b2)h
There are two identical bases, so their total area is ...
2A = (b1 +b2)h = (27 cm +6 cm)(8 cm) = 264 cm²
Lateral area
The lateral area of the prism is the area of the four rectangular faces. Each is 30 cm wide, and their total length is the perimeter of the base;
P = 27 cm +10 cm +6 cm +17 cm = 60 cm
lateral area = Ph = (60 cm)(30 cm) = 1800 cm²
Total surface area
The total surface area of the prism is the sum of the base area and the lateral area:
total area = base area + lateral area
total area = 264 cm² +1800 cm² = 2064 cm²
The surface area of the solid prism is 2064 cm².
