Question 128963
what is the area of parallegogram ABCD with vertices A(-4,-6),B(6,-6),C(-1,5),D(9,5)?
dont understand how to get the answer


{{{drawing(400,400,-5,10,-8,7,
graph(400,400,-5,10,-8,7),

line(-4,-6,6,-6), line(6,-6,9,5), line(-1,5,9,5), line(-1,5,-4,-6),

locate(-4,-6,"A(-4,-6)"),
locate(6,-6,"B(6,-6)"),
locate(-1,5,"C(-1,5)"),
locate(7,5,"D(9,5)"), grid(1)
)}}}


The formula for the area of a parallelogram
is

{{{A = (base)(height)}}}

We know the base is 10 units long, because the
bottom side extends from 4 units left of the
y-axis to 6 units right of the y-axis.  That's
a total of 10 units for the base.

Let's draw the height as a dotted line:

{{{drawing(400,400,-5,10,-8,7,
graph(400,400,-5,10,-8,7),

line(-4,-6,6,-6), line(6,-6,9,5), line(-1,5,9,5), line(-1,5,-4,-6),

locate(-4,-6,"A(-4,-6)"),
locate(6,-6,"B(6,-6)"),
locate(-1,5,"C(-1,5)"),
locate(7,5,"D(9,5)")
line(2.9,-6,2.9,-5), line(3.2,-4,3.2,-3), line(3.2,-2,3.2,-1), line(3.2,0,3.2,1),
line(3.2,2,3.2,3), line(3.2,4,3.2,5), grid(1)  )}}}

We see that the height extends from 6 units below the x-axis to 5 units
above the x-axis, so that is 11 units.

So

{{{A = (base)(height)}}} = {{{(10)(11)}}} = 110 square units.

Edwin</pre>