Check out the attached image. Each figure shows a different face or wall of the 3D object that is painted in red.
Figure 1 shows the front wall which is 10*24 = 240 sq cm
Figure 2 shows the back wall which is 10*24 = 240 sq cm
Figure 3 shows the left wall which is 10*27 = 270 sq cm
Figure 4 shows the right wall which is 10*27 = 270 sq cm
Figure 5 shows the top wall which is 24*27 = 648 sq cm
Figure 6 shows the bottom wall which is 24*27 = 648 sq cm
Each of those individual results is then added up to get:
240+240+270+270+648+648 = 2316
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Final Answer: 2316 square centimeters