A quadrilateral has vertices at (1,1), (6, 2), (5, 5),(3, 6). Find the area of the quadrilateral in cm.    

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aruv | High School Teacher | (Level 2) Valedictorian

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Let P(11) ,Q(6,2),R(5,5) and S(3,6) be the quadrilateral.Join P to R ad consider triangles PQR and  PRS.

area of triangle (PQR)+ area of triangle (PRS)=area of quadrilatera (PQRS)

`ar(DeltaPQR)=(1/2)|[1,1,1],[6,2,1],[5,5,1]|`

`=(1/2){1(2-5)-1(6-5)+1(30-10)}`

`=(1/2){-3-1+20}`

`=(1/2){16}=8` 

 `ar(DeltaPRS)=(1/2)|[1,1,1],[5,5,1],[3,6,1]|`

`=(1/2){1(5-6)-1(5-3)+1(30-15)}`

`=(1/2){-1-2+15}`

`=(1/2){12}`

`=6`

Thus

area of quadrlateralPQRS=`ar (DeltaPQR)+ar(DeltaPRS)`

`=8+6`

`=14` sq cm.

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