Question

Find the perimeter of the polygon with the given verices​

Answer 1

6.

Perimeter = 22

7.

Perimeter = 13 +
`√(89)`

Explanation:

Perimeter refers to sum of all the sides. Therefore, first we will find the length of sides using the given points by using the distance formula .

6.

Distance Formula :

Distance between points
`\left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right )` is equal to
`√(\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2)`

GH =
`√(\left ( 2-2 \right )^2+\left ( -3-4 \right )^2)=7`

HJ =
`√(\left ( -2-2 \right )^2+\left ( -3+3 \right )^2)=4`

JK =
`√(\left ( -2+2 \right )^2+\left ( 4+3 \right )^2)=7`

KG =
`√(\left ( 2+2 \right )^2+\left ( 4-4 \right )^2)=4`

So, Perimeter = 7 + 4 + 7 + 4 = 22

7.

UV =
`√(\left ( 3+2 \right )^2+\left ( 4-4 \right )^2)=5`

VW =
`√(\left ( 3-3 \right )^2+\left ( -4-4 \right )^2)=8`

UW =
`√(\left ( 3+2\right )^2+\left ( -4-4 \right )^2)=√(89)`

Therefore, perimeter = 5 + 8 +
`√(89)` = 13 +
`√(89)`

Answer 2

Explanation:

GH: You don't need the distance formula for this distance. The x value cancels and you get (4 - - 3) = 7 units.

HJ: HJ = sqrt( 2 - - 2)^2 + (-3 - - 3)^2 ) = 4 I didn't see the y values as being the same.

JK: No need for the formula here either. The x values cancel. JK = abs(-3 - 4)

JK = 7

KG = The distance formula is not needed here either. The y values cancel.

KG = abs(2 - - 2)= 4

The perimeter = 7 + 4 + 7 + 4 = 22

Problem 7

UV: No need for the formula for this segment. The y values cancel. UV = abs(-2 -3) = 5

VW: The x values will cancel. VW = abs(4 - - 4) = 8

WU: You are going to have to use the formula here.

WU = sqrt( (y2 - y1)^2 + (x2 - x1) )

y2 = 4

y1 = - 4

x2 = -2

x1 = 3

WU = sqrt( (4 - - 4)^2 + (-2 - 3)^2 )

WU = sqrt( (8)^2 + (-5)^2 )

WU = sqrt ( 64 + 25)

WU = sqrt (89)

The perimeter = 5+ 8 + sqrt(89)

or

The perimeter = 13 + sqrt(89)

or

The perimeter = 13 + 9.43

The perimeter = 22.43