What is the perimeter of a polygon with vertices at (-3, 1), (5, 1), (-3, 4), (5, 4)?

The perimeter of the polygon is 22.

Step-by-step explanation:

Let , , and the vertices of the polygon. From Geometry we know that number of side of polygons equals their number of vertices, then we notice that a quadrilateral is here. In addition, we conclude that such quadrilateral is a rectangle:

1)

2)

3)

4)

Hence, we find that and .

Then we find all lengths of the rectangle by Pythagorean Theorem:

By Geometry, we conclude that and .

Then, the perimeter of the rectangle (), dimensionless, is defined by the following formula:

(Eq. 1)

Where:

- Shortest length, dimensionless.

- Longest length, dimensionless.

If we know that and , then the perimeter of the rectangle is:

The perimeter of the polygon is 22.

you are saying it as if a fact, not a question, but yes, you would be correct? ; )

step-by-step explanation:

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet