Answer:
The perimeter of the pentagon is;
29 units
Step-by-step explanation:
Let A, B, C, D, and E represent the vertices of the pentagon
The "x" and "y" coordinates of the vertices of the pentagon are given as follows;
A(-6, 2), B(-2, -2), C(5, -2), D(5, 2), E(-2, 5)
The length of the sides between each pair of coordinates can be found using the following formula;
[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]
Therefore, we have;
Length of segment AB = √((-2 - (2))² + (-2 - (-6))²) = 4·√2
Length of segment BC = √((-2 - (-2))² + (5 - (-2))²) = 7
Length of segment CD = √((5 - 5)² + (2 - (-2))²) = 4
Length of segment DE = √((5 - 2)² + (-2 - 5)²) = √58
Length of segment EA = √((5 - (2))² + (-2 - (-6))²) = 5
The length of the perimeter of the pentagon = 5+√58 + 4 + 7 + 4·√2 ≈ 29.2726273554 ≈ 29
The length of the perimeter of the pentagon ≈ 29.
