Find the area of quadrilateral abcd whose vertices are
Asked by admin @ in Math viewed by 290 People
Find the area of quadrilateral ABCD whose vertices are A(-3,-1) B(-2,-4) C(4,-1) D(3,4) ?????
COORDINATE GEOMETRY QUESTION .
Answered by admin @
A(-3,1), B(-2,-4), C(4,-1), D(3,4) are the vertices of quadrilateral ABCD
Let AC be the diagonal of quad ABCD
therefore, ar of quad ABCD= ar triangle ABC+ ar triangle ADC
ar of triangle ABC= 1/2[x1(y2-y3) -x2(y3-y1) -x3(y1-y2)]
= 1/2[ (-3) (-4+1) + (-2) (-1+1) +4(-1+4) ]
=1/2[9+0+12]
=21/2 sq units
ar of triangle ADC= 1/2[ (-3) (4+1) + 3(-1+1) + 4(-1-4)]
=1/2[-15+0-20]
= -35/2 sq units (since area cant be negative so area of triangle ADC=35/2 sq units)
Hence ar of quadrilateral ABCD= 21/2 + ( 35/2)
=56/2= 28 sq units
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