Question

find the area of a quadrilateral whose vertices, taken in order are (-4,-2),(-3,-5),(0,-5) and (2,-2)

Answer 1

 Area of Quadrilateral ABCD = Area of Triangle ABD + Area of Triangle BCD     (1)

Using formula to find area of triangle:

Area of △ABD = 12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))

⇒ Area of △ABD=12(−4(−5−3)−3(3−(−2))+2(−2−(−5)))

=12(32−15+6)=12(23)=11.5 sq units             (2)

Again using formula to find area of triangle:

Area of △BCD = 12(x1(y2−y3)+x2(y3−y1)+x3(y1−y2))

⇒ Area of △BCD=12(−3(−2−3)+3(3−(−5))+2(−5−(−2))

=12(15+24−6)=12(33)=16.5 sq units          (3)

Putting (2) and (3) in (1), we get

Area of Quadrilateral ABCD = 11.5 + 16.5 = 28 sq units

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