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=√((x_2-x_1)^2+(y_2-y_1)^2)`

now, we can plug values

`AB=√((4+2)^2+(3-0)^2)`

`AB=3√(5)`

Since, this is parallelogram

so, opposite sides are equal

so,

`CD=AB=3√(5)`

Calculation of AD:

point A =(-2,3)

point D=(-5,2)

we can use distance formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

now, we can plug values

`AD=√((-5+2)^2+(2-3)^2)`

`AD=√(10)`

Since, this is parallelogram

so, opposite sides are equal

so,

`BC=AD=√(10)`

Calculation of AE:

point A=(-2,3)

point E=(-3,1)

we can use distance formula

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

now, we can plug values

`AE=√((-3+2)^2+(1-3)^2)`

`AE=√(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√(5)+√(10)+3√(5)+√(10)`

`=6√(5)+2√(10)`...........Answer

(b)

we can use area of parallelogram formula

`A=AE* CD`

we can plug values

`A=√(5)* 3√(5)`

`A=15`............Answer