here when the prism is cut by two perpendicular lines we will have four prisms and each will have equal surface area...
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now each cut prism will have 6 parts. A,B,C,D(as rectangles), top , bottom(as two triangles having one common side)...
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now solving the bottom part :
we can see that the bottom part can be broken into two triangles.
the triangle in green will form equilateral triangle as the prism is regular and each side(12 cm) will make 60` with center and as other two sides will also be equal..
so area = √ 3/4 (12)^2
also area of yellow triangle will be = 1/2 area of green triangle = 1/2 *√ 3/4 *12^2
= 54√ 3
also area of top = area of bottom = 54√ 3
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area of part A= 24*12 = 288
part B= 24*12= 288
part C=24*6= 144
part D = 24*6√3 (height of equilateral triangle) = 144√ 3
top+botom= 108√ 3
so total area of one piece = 720 + 252√ 3
therefore total surface area of four prism = 4* (720 + 252√ 3)
= 2880 + 1008√3 cm^2 answer. = option B