Question

Q. A prism has a regular hexagonal base with side 12cm.
If height of prism is 24cm, and it is cut into 4
equal parts by 2 perpendicular cuts as shown, find
the sum of TSA of four parts ?
(a) 1725+432√3
(b)2880 - 432√3
(c) 2880 + 1008√3
(d) 1728 + 1008√3

Answer 1

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Ayush Upadhyaya

asked in Verbal Ability Dec 17, 2018

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A prism has a regular hexagonal base whose side is 12cm.The height of the prism is 24cm.It is cut into 4 equal parts by 2 perpendicular cuts as shown.What is the sum of the total surface area of the four parts?

(A)1728+4323–√

(B)2880+10083–√

(C)2880+4323–√

(D)1728+10083–√

Answer is given to be (B) but I was unable to understand the solution.

Can someone give easy solution to this?

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here when the prism is cut by two perpendicular lines we will have four prisms and each will have equal surface area...

.

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