Question

Please answer question no. 9 ...

Answer 1

$Area \: of \: triangle \: = \: \dfrac{1}{2} \: | x_{1}( y_{2} - y_{3}) + x_{2}( y_{3} - y_{1} ) + x_{3}( y_{1} - y_{2} ) |$

Continuing the Attachment ..

We have

Area of $\triangle$PQR = $\dfrac{21}{2}$ sq. units

________ (eq 1)

Also,

Area of $\triangle$PSR = $\dfrac{-35}{2}$ sq. units

__________ (eq 2)

But area can't be negative.

So,

Area of $\triangle$PSR = $\dfrac{35}{2}$ sq. units

__________ (eq 3)

To find Area of quadrilateral PQRS we have to add the area of $\triangle$PQR and area of $\triangle$PSR.

i.e.

Area of quadrilateral PQRS = Area of $\triangle$PQR + Area of $\triangle$PSR

=> $\dfrac{21}{2}$ + $\dfrac{35}{2}$

=> $\dfrac{56}{2}$

=> 28 sq. units

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