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CAT 2018 Slot 1 — QA Question 18

Basics of QuadrilateralsEasy

In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is

Answer & solution

  • A

    12√3

  • B

    24√3

  • C

    18√3

  • 32√3

Solution

Area of parallelogram = base × height
∴ A(□ABCD) = CD × AP
∴ 72 = 9 × AP
∴ AP = 8

Consider ∆APD.

PD = 162-82 = 8√3

A(APD) = 1/2 × 8√3 × 8 = 32√3 sq.cm.

Hence, option (d).

CAT 2018 Slot 1 QA Q18: In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P — Solution | TheCATExam