The vertices of a quadrilateral is given as A( −4,5 ), B( 0,7 ), C( 5,−5 ) and D( −4,−2 ).
Plot the given points on Cartesian plane and join AB, BC, CD and AD.
The quadrilateral formed after joining these points is shown below,
![](https://search-static.byjusweb.com/question-images/scholr/scholr-acadecraft/Images/HTML_47618_1.JPG)
The above figure shows the quadrilateral formed by given vertices.
Draw a diagonal AC, then the area of the quadrilateral ABCD is,
area( ABCD )=area( ΔABC )+area( ΔACD )
It is known that the area of triangle with vertices ( x 1 , y 1 ), ( x 2 , y 2 ) and ( x 3 , y 3 ) is,
Area= 1 2 | x 1 ( y 2 − y 3 )+ x 2 ( y 3 − y 1 )+ x 3 ( y 1 − y 2 ) |
So, the area of ΔABC is,
area of ΔABC= 1 2 | −4( 7+5 )+0( −5−5 )+5( 5−7 ) | = 1 2 | −4( 12 )+5( −2 ) | = 1 2 | −58 | =29 unit 2
The area of ΔACD is,
area of ΔACD= 1 2 | −4( −5+2 )+5( −2−5 )+( −4 )( 5+5 ) | = 1 2 | −4( −3 )+5( −7 )−4( 10 ) | = 1 2 | −63 | = 63 2 unit 2
The area of the quadrilateral is,
area( ABCD )=29+ 63 2 = 58+63 2 = 121 2 unit 2
Therefore, the area of the quadrilateral ABCD is 121 2 unit 2 .