Question

Draw a quadrilateral ABCD whose vertices are A(−4,− 3) , B (5,−3) , C ( 5,3) and D(−4,3). What is the special name of the quadrilateral ABCD? Find its area.

Answer 1

Step-by-step explanation:

The coordinates of ABCD are A(−3,−1),B(−2,−4),C(4,−1),D(3,4).

Area of quadrilateral ABCD = Area of triangle ABC + Area of triangle ACD

Area of triangle = 21∣[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]∣

Area of triangle ABC = 21∣[−3(−4+1)−2(−1+1)+4(−1+4)]∣

=21∣[9+12]∣=221 sq. units

Area of triangle ACD = 21∣[−3(−1−4)+4(4+1)+3(−1+1)]∣

=21∣[15+20]∣=235 sq. units

Therefore, Area of quadrilateral ABCD = 221+235=28 sq. units