Given a(-2,0); b(2,0); c(4,3); d(0,4); and e(-4,3) find the area and perimeter

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

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;

distance between (-4,3) & (-2,0) =(4,3) & (2,0) =

=

=

=

=√13

distance between (0,4) & (4,3) =(0,4) & (-4,3) =

=

=

=

=√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

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