Question

Find the perimeter of the polygon with the vertices X(−1, 3), Y(3, 0), and Z(−1,−2). Round your answer to the nearest hundredth

Answer 1

The perimeter of the polygon is
`P=14.47\ units`

Explanation:

we know that

The perimeter is the sum of the length sides of the polygon

In this problem

P=XY+YZ+XZ

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

step 1

Find the distance XY

we have

X(−1, 3), Y(3, 0)

substitute

`d=\sqrt{(0-3)^(2)+(3+1)^(2)}`

`d=√(25)`

`dXY=5\ units`

step 2

Find the distance YZ

we have

Y(3, 0), Z(−1,−2)

substitute

`d=\sqrt{(-2-0)^(2)+(-1-3)^(2)}`

`d=√(20)`

`dYZ=4.47\ units`

step 3

Find the distance XZ

we have

X(−1, 3), Z(−1,−2)

substitute

`d=\sqrt{(-2-3)^(2)+(-1+1)^(2)}`

`d=√(25)`

`dXZ=5\ units`

step 4

Find the perimeter

P=XY+YZ+XZ

`P=5+4.47+5=14.47\ units`