Question

Find the perimeter AND area of the parallelogram ABCD. Show all work

Answer 1

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

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

now, we can plug values

$AB=\sqrt{(4+2)^2+(3-0)^2}$

$AB=3\sqrt{5}$

Since, this is parallelogram

so, opposite sides are equal

so,

$CD=AB=3\sqrt{5}$

Calculation of AD:

point A =(-2,3)

point D=(-5,2)

we can use distance formula

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

now, we can plug values

$AD=\sqrt{(-5+2)^2+(2-3)^2}$

$AD=\sqrt{10}$

Since, this is parallelogram

so, opposite sides are equal

so,

$BC=AD=\sqrt{10}$

Calculation of AE:

point A=(-2,3)

point E=(-3,1)

we can use distance formula

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

now, we can plug values

$AE=\sqrt{(-3+2)^2+(1-3)^2}$

$AE=\sqrt{5}$

(a)

we know that

perimeter of a parallelogram is sum of all sides

so,

perimeter is

$=AB+BC+CD+DA$

now, we can plug values

$=3\sqrt{5}+\sqrt{10}+3\sqrt{5}+\sqrt{10}$

$=6\sqrt{5}+2\sqrt{10}$...........Answer

(b)

we can use area of parallelogram formula

$A=AE\times CD$

we can plug values

$A=\sqrt{5}\times 3\sqrt{5}$

$A=15$............Answer