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. $2+12\sqrt{2}$ units

B. $7+2\sqrt{2}$ units

C. $10+4\sqrt{2}$ units

D. $12+2\sqrt{2}$ units

E. $12+4\sqrt{2}$ units

Answer: E. $12+4\sqrt{2}$ units

Step-by-step 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)

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

$d=2\sqrt{2}$

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)

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

$d=2\sqrt{2}$

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 = $5+2\sqrt{2}+5+2\sqrt{2}+2$

P = $12+4\sqrt{2}$

Perimeter of polygon LMNPQ is $12+4\sqrt{2}$ units