Find the perimeter of the pentagon with vertices M(-2,5), N(2,5), P (5, 3),

Q(5,0), and R(3, 3). Do not round before calculating the perimeter. After calculating

the perimeter, round to the nearest tenth.

The perimeter is

units.

Question

06-01-2022
Mathematics

Answered

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Find the perimeter of the pentagon with vertices M(-2,5), N(2,5), P (5, 3),

Q(5,0), and R(3, 3). Do not round before calculating the perimeter. After calculating

the perimeter, round to the nearest tenth.

The perimeter is

units.

Sagot :

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xero099 xero099 · Answer 1 · 2022-01-13T05:53:25-05:00

The perimeter of the pentagon is approximately 19.6.

Procedure - Determination of the perimeter of a pentagon

In this question we must plot the locations of each vertex on a Cartesian plane to determine the line segments that form the perimeter, whose lengths are determined by Pythagorean theorem and sum the resulting values to find the perimeter.

According to the image attached below, the line segments of the pentagon are MN, NP, PQ, QR and RM. By Pythagorean theorem we have the following lengths:

Line segment MN

[tex]l_{MN} = \sqrt{[2-(-2)]^{2}+(5-5)^{2}}[/tex]

[tex]l_{MN} = 4[/tex]

Line segment NP

[tex]l_{NP} = \sqrt{(5-2)^{2}+(3-5)^{2}}[/tex]

[tex]l_{NP} = \sqrt{13}[/tex]

Line segment PQ

[tex]l_{PQ} = \sqrt{(5-5)^{2}+(0-3)^{2}}[/tex]

[tex]l_{PQ} = 3[/tex]

Line segment QR

[tex]l_{QR} = \sqrt{(3-5)^{2}+(3-0)^{2}}[/tex]

[tex]l_{QR} = \sqrt{13}[/tex]

Line segment RM

[tex]l_{RM} = \sqrt{(-2-3)^{2}+(5-3)^{2}}[/tex]

[tex]l_{RM} = \sqrt{29}[/tex]

And the perimeter of the pentagon is:

[tex]p = l_{MN} + l_{NP} + l_{PQ} + l_{QR} + l_{RM}[/tex] (1)

[tex]p = 4 + \sqrt{13} + 3 + \sqrt{13} + \sqrt{29}[/tex]

[tex]p = 7 + 2\sqrt{13} + \sqrt{29}[/tex]

[tex]p \approx 19.6[/tex]

The perimeter of the pentagon is approximately 19.6. [tex]\blacksquare[/tex]

To learn more on pentagons, we kindly invite to check this verified question: https://brainly.com/question/27476