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CAT 2017 Slot 2 — QA Question 16

Basics of Mensuration/PrismEasy

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 equal in 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

Answer & solution

  • A

    1300

  • B

    1340

  • 1480

  • D

    1520

Solution

Let us draw the base of the vertical pillar as shown below

In the above figure EF = AB = 10 cm

Also, as AD = BC, by rule of symmetry
DE = FC

Now DC = DE + EF + FC

Let DE = FC = x

20 = x + 10 + x
⇒ 2x + 10 = 20
⇒ x = 5

Now in ∆AED, AE = 12 cm and DE = 5 cm

∴ AD = 52+122=13

Also given AD = BC

∴ BC = 13 units

Now, total surface area of vertical pilar with base ABCD = Area of Rectangle with side AB and side (Height) 20 cm + Area of Rectangle side AD and side (Height) 20 cm + Area of Rectangle with side BC and side (Height) 20 cm + Area of Rectangle with side DC and side (Height) 20 cm + 2 × Area of Trapezium ABCD

⇒ 10 × 20 + 13 × 20 + 13 × 20 + 20 × 20 + 2 × 12 × (20 + 10) × 12
⇒ 200 + 260 + 260 + 400 + 360
⇒ 1480 sq.cm.

Hence, option (c).

CAT 2017 Slot 2 QA Q16: The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 — Solution | TheCATExam