Question

Polygon LMNPQ is shown on the coordinate grid. What is the preempted of polygon LMNPQ

Answer 1

The question is incomplete. Here is the complete question.

Polygon LMNPQ is shown on the coordinate grid. What is the perimeter of polygon LMNPQ?

A.
`2+12√(2)` units

B.
`7+2√(2)` units

C.
`10+4√(2)` units

D.
`12+2√(2)` units

E.
`12+4√(2)` units

Answer: E.
`12+4√(2)` units

Explanation: Perimeter of a figure is the sum of all of its sides.

The polygon is drawn on a plane. The distance between a pair of points will give that side its measure.

Distance of two points is calculated as

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

Segment MN:

Coordinates: M (2,4) and N (5,8)

`d=\sqrt{(5-2)^(2)+(8-4)^(2)}`

d = 5

Segment ML:

Coordinates: M (2,4) and L (4,2)

`d=\sqrt{(2-4)^(2)+(4-2)^(2)}`

`d=2√(2)`

Segment NP:

Coordinates: N (5,8) and P (8,4)

`d=\sqrt{(5-8)^(2)+(8-4)^(2)}`

d = 5

Segment PQ:

Coordinates: P (8,4) and Q (6,2)

`d=\sqrt{(8-6)^(2)+(4-2)^(2)}`

`d=2√(2)`

Segment LQ:

Coordinates: L (4,2) and Q (6,2)

`d=\sqrt{(6-4)^(2)+(2-2)^(2)}`

d = 2

Calculating perimeter (P):

P = MN + ML + NP + PQ + LQ

P =
`5+2√(2)+5+2√(2)+2`

P =
`12+4√(2)`

Perimeter of polygon LMNPQ is
`12+4√(2)` units