Maths / Coordinate Geometry / Area of Triangle Using Coordinate

QUESTION

If A(-5,7), B(-4,-5), C(-1,-6) and D(4,5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

EXPLANATION
Explain TypeExplanation Content
Text

By joining B to D, you will get two triangle ABD and BCD.

Now          the area of $\Delta ABD=\frac {1}{2}\left [ -5(-5-5)+(-4)(5-7)+4(7+5) \right ]$

$=\frac {1}{2}(50+8+48)=\frac {106}{2}=53$   square units

Also,     the area of  $\Delta BCD=\frac {1}{2}\left [ -4(-6-5)-1(5+5)+4(-5+6) \right ]$

$=\frac {1}{2}(44-10+4)=19$  square units

So, the area of quadrilateral  $ABCD=53+19=72$   square units.

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