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CAT 2017 [slot 2] Question with solution 16

Question 50:
The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is
  1. 1300
  2. 1340
  3. 1480
  4. 1520
Option: 3
Explanation:

Given, the non-parallel sides are equal.

Let the non-parallel sides be $x$ cm each

$x = \sqrt { 12 ^ { 2 } + 5 ^ { 2 } } = 13$

So, we have 6 faces, two are trapezoid faces and 4 are rectangular faces.

Area of 2 trapeziums

$= 2 \left[ \frac { 1 } { 2 } ( 12 ) ( 10 + 20 ) \right] = 360 \mathrm { cm } ^ { 2 }$

$= 2 [ 13 \times 20 ] + 20 ( 20 ) + 10 ( 20 ) = 1120 \mathrm { cm } ^ { 2 }$

Total area $= 1120 + 360 = 1480 \mathrm { cm } ^ { 2 }$


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