Since, this is parallelogram
so, opposite sides are equal
We will find value of sides
Calculation of AB:
we are given point A=(-2,3)
point B=(4,0)
we can use distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
now, we can plug values
[tex]AB=\sqrt{(4+2)^2+(3-0)^2}[/tex]
[tex]AB=3\sqrt{5}[/tex]
Since, this is parallelogram
so, opposite sides are equal
so,
[tex]CD=AB=3\sqrt{5}[/tex]
Calculation of AD:
point A =(-2,3)
point D=(-5,2)
we can use distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
now, we can plug values
[tex]AD=\sqrt{(-5+2)^2+(2-3)^2}[/tex]
[tex]AD=\sqrt{10}[/tex]
Since, this is parallelogram
so, opposite sides are equal
so,
[tex]BC=AD=\sqrt{10}[/tex]
Calculation of AE:
point A=(-2,3)
point E=(-3,1)
we can use distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
now, we can plug values
[tex]AE=\sqrt{(-3+2)^2+(1-3)^2}[/tex]
[tex]AE=\sqrt{5}[/tex]
(a)
we know that
perimeter of a parallelogram is sum of all sides
so,
perimeter is
[tex]=AB+BC+CD+DA[/tex]
now, we can plug values
[tex]=3\sqrt{5}+\sqrt{10}+3\sqrt{5}+\sqrt{10}[/tex]
[tex]=6\sqrt{5}+2\sqrt{10}[/tex]...........Answer
(b)
we can use area of parallelogram formula
[tex]A=AE\times CD[/tex]
we can plug values
[tex]A=\sqrt{5}\times 3\sqrt{5}[/tex]
[tex]A=15[/tex]............Answer
