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MAVERICK [17]
3 years ago
9

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

Mathematics
1 answer:
Nadya [2.5K]3 years ago
7 0

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: <u>Perimeter</u> 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

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