Q57 of 66 Page 7

If A (-3, 5), B (-2,-7), C (1,-8) and D (6, 3) are the vertices of a quadrilateral ABCD, find its area.(CBSE 2014)

Given vertices of a quadrilateral ABCD are A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3)


Area of the quadrilateral ABCD = Area of ∆ABC + Area of ∆ACD


Area of the triangle having vertices (x1,y1), (x2,y2) and (x3,y3)


= |x1(y2-y3)+x2(y3-y1)+x3(y1-y2)|


Area of ∆ABC = | − 3[ − 7 − ( − 8 )] + ( − 2) ( − 8 – 5 ) + 1 [ 5 − (− 7) ] |


= | − 3 + 26 + 12 |


=sq. units


Area of ∆ACD = |− 3( − 8 – 3 ) + 1( 3 – 5 ) + 6[ 5 − ( − 8 ) ] |


= | 33 – 2 + 78 |


= sq. units


Area of the quadrilateral ABCD = + = 72 sq. units


∴Hence, the area of the quadrilateral is 72 sq. units.

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