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.