Question 702082
{{{drawing(300,300,-3,5,-4,4,
grid(1),
blue(circle(-2,2,0.15)),blue(circle(-1,1,0.15)),
blue(circle(3,-2,0.15)),blue(circle(4,1,0.15)),
blue(line(-2,2,-1,1)),blue(line(4,1,-2,2)),
blue(line(3,-2,-1,1)),blue(line(4,1,3,-2)),
green(line(-1,1,4,1))
)}}} The horizontal (green) segment connecting (-1,1) to (4,1) splits the quadrilateral into two triangles, and it can be considered the base of both triangles.
Its length is {{{b=5}}}
Their heights are {{{h[1]=1}}} and {{{h[2]=3}}}
Their areas are
{{{area[1]=(1/2)*5*1}}} and {{{area[2]=(1/2)*5*3}}}
The area of the quadrilateral is the sum:
{{{area=(1/2)*5*1+(1/2)*5*3}}} --> {{{area=(1/2)*5*(1+3)}}} --> {{{area=(1/2)*5*4}}} --> {{{highlight(area=10)}}}