Question

In the given figure PA/AQ=PB/BR=3. IF the area of triangle pqr is 32cm^2.then find the area of the quadrilateral aqrb.​

Answer 1

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Answer 2

Given:

PA/AQ=PB/BR=3

triangle PQR is 32cm²

quadrilateral AQRB = ?

$\text { We have, } \triangle \mathrm{PQR} \sim \triangle \mathrm{PAB}$

$\text { ( } \therefore \angle \mathrm{P} \text { is common and } \mathrm{PA} / \mathrm{PQ}=\mathrm{PB} / \mathrm{PR} \text { ) }$

$\frac{area\ (\Delta P Q R)}{area\ (\Delta P A B)} = \frac{PQ^{2} }{PA^{2}}$

$\frac{32}{\text { area }(\Delta P A B)}=\frac{(4 k)^{2}}{(3 k)^{2}}=\frac{16 k^{2}}{9 k^{2}}$

$\text { area } \Delta P A B=18 \mathrm{~cm}^{2}$

$\therefore \text { area of quadrilateral } A Q R B$

$=\text { area of } \triangle P Q R \text {-area of } \triangle P A B$

$=32-18$

$=14 \mathrm{~cm}^{2}$

Hence the quadrilateral AQRB is 14 cm².