Find the area of the quadrilateral whose vertices are A(-4, 5), B(0, 7), C(5, -5) and D(-4, -2).

Given: The vertices of the quadrilateral are A(-4, 5), B(0, 7), C(5, -5) and D(-4, -2).


Formula: Area of a triangle



Area of quadrilateral ABCD = Area of Δ ABC + Area of Δ ADC


Area of Δ ABC




= –29


Taking modulus ( area is always positive),


Area of Δ ABC = 29 sq. units …..(1)


Area of Δ ADC



= 31.5 sq. units …..(2)


From 1 and 2,


Area of quadrilateral ABCD = 29 + 31.5


= 60.5 square units.


Therefore, the area of quadrilateral ABCD is 60.5 square units.


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