Question
The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.
Answer: Option C
:
C
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:
C
Consider the pointsÂ
A(−4,−2),B(−3,−5),C(3,−2) and D(2,3).A(△)=12×|x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|
∴ Area of △ABCÂ
  =12|(−4)(−5+2)−3(−2+2)+3(−2+5)|  =12|20−8−6+15|=212A(â–³ABC)=10.5 sq. unitsÂ
Similarly, area of  △ACD
  =12|(−4)(−2−3)+3(3+2)+2(−2+2)|  =12|20+15|=352A(â–³ACD)=17.5 sq. unitsÂ
Area of quadrilateral ABCD=A(â–³ABC)+A(â–³ACD)               =(10.5+17.5)=28 sq. unitsÂ
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