Answer:
The area is 20 and perimeter is 19.4
Step-by-step explanation:
The given points will be plot on graph as shown in figure-1
To calculate the area of this figure,
we divide this pentagon into 5 equal parts (figure-2)
we calculate area of only one part and then multiply with 5 to get area of pentagon.
we can see in figure-2 , base is shown by green line which is '4' and height is shown by red line which is '2'
so, the area of triangle is calculated by [tex]\frac{1}{2}\times\text{height}\times{base}[/tex]
[tex]A=\frac{1}{2}\times2\times4[/tex]
[tex]A=4[/tex]
therefore, the total area of pentagon is A=5*4 = 20
To calculate the perimeter of pentagon;
Parameter = Add all the sides of pentagon
to find the length of sides of polygon by using distance formula;
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
distance between (-4,3) & (-2,0) =(4,3) & (2,0) = [tex]\sqrt{(-2-(-4))^2+(0-3)^2}[/tex]
=[tex]\sqrt{(2)^2+(-3)^2}[/tex]
=[tex]\sqrt{4+9}[/tex]
=[tex]\sqrt{13}[/tex]
=√13
distance between (0,4) & (4,3) =(0,4) & (-4,3) = [tex]\sqrt{(4-(0))^2+(3-4)^2}[/tex]
=[tex]\sqrt{(4)^2+(1)^2}[/tex]
=[tex]\sqrt{16+1}[/tex]
=[tex]\sqrt{17}[/tex]
=√17
and distance between (-2,0) & (2,0) is 4
So, Parimeter 'P' ;
P= 2*√17 + 2*√13 + 4
P= 2*√17 + 2*√13 + 4
P= 8.246 + 7.21 + 4
P = 19.4
Hence area is 20 and perimeter is 19.4
