I need help in solving this

Admire the shape and you notice:

Total Surface Area = (2* Surface area of cylinder) + (2* Area of Trapezium) + (2* Area of Rectangle without circles) + (Area of small Rectangle at the top) + (Area of big Rectangle at Bottom).

Area of cylinder = πrh + πr^2.
Diameter = 18m, r = 18/2 = 9m, h = long = 26m π = 3.14
Substituting = 3.14 * 9* 26 + 3.14*9*9 = 989.1 m2. Using a calculator.

Area of Trapezium = 1/2 * (Sum of parallel sides) * height
      = 1/2 * ( 48 + 62) * 40
   = 1/2 * ( 110) * 40 = 110 *20 = 2200 m2.

Area of rectangle without circle = Area of rectangle - Area of circle from cylinder
   = (42*34) - (3.14*9*9) = 1428 - 254.34 = 1173.66 m2.

Area of small rectangle at the top = 48 * 34 = 1632 m2

Area of Big rectangle at bottom = 62 * 34 = 2108 m2.

Using the stated formula above:
Total surface area of composite = 2*989.1 + 2*2200 + 2*1173.66 + 1632 + 2108
      = 1978.2+ 4400 + 2347.32 + 1632 + 2108
Using your calculator

Total surface area = 12 465.52 m2.

Cheers.

FirstSineOfMadness FirstSineOfMadness · Answer 2 · 2014-11-25T13:52:42-05:00

Sorry this is so late, I had done out all my work a couple minutes after the question was asked but was unable to answer until now due to technical difficulties.
I also got a different number than the other answered, so here's mine:

Area of the small base of the trapezoid:
48*34=1632
Area of the larger base:
62*34=2108
Area of the top and bottom of the figure:
(62+48)/2*40=2200*2=4400
The space on the remaining sides that are covered by the cylinders is made up for by the ends of the cylinders themselves, so it is just
42*34=1428*2=2856
The remaining surface area of the cylinders is 2pi*r*h
2pi*9*26=468pi*2=936pi
Totaling the numbers without pi gets 10996
Add 936pi (about 2940) to that to get 13936
Final answer: about 13936 m^2
Again, sorry the answer is so late, I was unable to submit it earlier.
I just thought I should add my input in case it is needed.
Hope I helped :)