Question

Given A(-2,0); B(2,0); C(4,3); D(0,4); and E(-4,3) find the area and perimeter

Answer 1

The area is 20 and perimeter is 19.4

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
`(1)/(2)*\text{height}*{base}`

`A=(1)/(2)*2*4`

`A=4`

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;

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

distance between (-4,3) & (-2,0) =(4,3) & (2,0) =
`√((-2-(-4))^2+(0-3)^2)`

=
`√((2)^2+(-3)^2)`

=
`√(4+9)`

=
`√(13)`

=√13

distance between (0,4) & (4,3) =(0,4) & (-4,3) =
`√((4-(0))^2+(3-4)^2)`

=
`√((4)^2+(1)^2)`

=
`√(16+1)`

=
`√(17)`

=√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