CAT 2017 [slot 2] Question with solution 16

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