we know that
To find the area of a rhombus, multiply the lengths of the two diagonals and divide by two
so
[tex]A=\frac{1}{2}(d1*d2)[/tex]
where
d1 and d2---------> are the lengths of the two diagonals
In this problem the diagonals are
AC and DB
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance AC
[tex]A(-1,4)\ C(-1,0)[/tex]
substitute in the formula
[tex]d=\sqrt{(0-4)^{2}+(-1+1)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]dAC=4\ units[/tex]
Step 2
Find the distance DB
[tex]D(-5,2)\ B(3,2)[/tex]
substitute in the formula
[tex]d=\sqrt{(2-2)^{2}+(3+5)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(8)^{2}}[/tex]
[tex]dDB=8\ units[/tex]
Step 3
Find the area of the rhombus
[tex]A=\frac{1}{2}(d1*d2)[/tex]
we have
[tex]d1=dAC=4\ units[/tex]
[tex]d2=dDB=8\ units[/tex]
substitute the values
[tex]A=\frac{1}{2}(4*8)=16\ units^{2}[/tex]
therefore
the answer is
[tex]16\ units^{2}[/tex]
