The base of a vertical pillar with uniform cross section is a trapezium

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

Answer

Given, the non-parallel sides are equal. Let the non-parallel sides be x cm each.

x2 = 122 + 52

x = 13

So, there are 6 faces, two are trapezoid faces and 4 are rectangular faces.

Area of 2 trapeziums = 2 × ½(12)(10+20) = 360 cm2

Area of 4 rectangles = 2 × (13 × 20) + 20 × 20 + 10 × 20 = 1120 cm2

Total area = 1120 + 360 = 1480 cm2 

The correct option is C.