CAT 2018 Question Paper Shift 1 Solved Paper

Question : 69 of 100

Marks: +1, -0

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
Options

24 $√3$
12 $√3$
18 $√3$
32 $√3$

Validate

Solution:

Area of the parallelogram

{ABCD}=(

base

)

(height)

=( {CD})( {AP})=72 {sq.cm}

( {CD})( {AP})=729( {AP})=72=> {AP}=8

D P=√{A D^{2}-A P^{2}}=√{16^{2}-8^{2}}=8 √{3}

Area of triangle

A P D=\;{1}/{2}(A P)(P D)=32 √{3}

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