Respuesta :
The perimeter of the given pentagon is 26 units.
What is the perimeter of a pentagon?
The perimeter of a pentagon is the sum of the length all the sides of the pentagon.
Given, the coordinates of a pentagon ABCDE are A(-5,4),B (1,4),C(1,-1), D(-2,-5) and E(-5,-1).
For the given pentagon:
The length of AB is
[tex]\sqrt{(4 - 4)^{2} + (1 - (- 5)^{2}} units\\= \sqrt{(1 + 5)^{2}} units\\= 6 units[/tex]
The length of BC is
[tex]\sqrt{(- 1 - 4)^{2} + (1 - 1)^{2}} units\\= \sqrt{(- 5)^{2}} units\\= 5 units[/tex]
The length of CD is
[tex]\sqrt{(- 5 - (- 1))^{2} + (- 2 - 1)^{2}} units\\= \sqrt{(- 4)^{2} + (- 3)^{2} } units\\= \sqrt{16 + 9} units\\ = \sqrt{25} units\\= 5 units[/tex]
The length of DE is
[tex]\sqrt{(- 1 - (- 5))^{2} + (- 5 - (- 2)^{2}} units\\= \sqrt{(4)^{2} + (- 3)^{2} } units\\= \sqrt{16 + 9} units\\ = \sqrt{25} units\\= 5 units[/tex]
The length of EA is
[tex]\sqrt{(- 1 - 4))^{2} + (- 5 - (- 5)^{2}} units\\= \sqrt{(- 5)^{2}} units\\= 5 units[/tex]
Therefore, the perimeter of the pentagon ABCDE is
[tex]= (5 + 5 + 5 + 5 + 6) units\\= 26 units[/tex]
Learn more about the perimeter of a pentagon here: https://brainly.com/question/1592650
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