Find the perimeter and area of the parallelogram abcd. show all work

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

now, we can plug values

Since, this is parallelogram

so, opposite sides are equal

so,

Calculation of AD:

point A =(-2,3)

point D=(-5,2)

we can use distance formula

now, we can plug values

Since, this is parallelogram

so, opposite sides are equal

so,

Calculation of AE:

point A=(-2,3)

point E=(-3,1)

we can use distance formula

now, we can plug values

(a)

we know that

perimeter of a parallelogram is sum of all sides

so,

perimeter is

now, we can plug values

...........Answer

(b)

we can use area of parallelogram formula

we can plug values

............Answer

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2